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A333221
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Irregular triangle read by rows where row n lists the set of STC-numbers of permutations of the prime indices of n.
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24
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0, 1, 2, 3, 4, 5, 6, 8, 7, 10, 9, 12, 16, 11, 13, 14, 32, 17, 24, 18, 20, 15, 64, 21, 22, 26, 128, 19, 25, 28, 34, 40, 33, 48, 256, 23, 27, 29, 30, 36, 65, 96, 42, 35, 49, 56, 512, 37, 38, 41, 44, 50, 52, 1024, 31, 66, 80, 129, 192, 68, 72, 43, 45, 46, 53, 54, 58
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OFFSET
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1,3
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COMMENTS
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This is a permutation of the nonnegative integers.
The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. We define the composition with STC-number k to be the k-th composition in standard order.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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Reading by columns gives:
0 1 2 3 4 5 8 7 10 9 16 11 32 17 18 15 64 21 128 19
6 12 13 24 20 22 25
14 26 28
34 33 256 23 36 65 42 35 512 37 1024 31 66 129 68 43
40 48 27 96 49 38 80 192 72 45
29 56 41 46
30 44 53
50 54
52 58
The sequence of terms together with the corresponding compositions begins:
0: () 24: (1,4) 27: (1,2,1,1)
1: (1) 18: (3,2) 29: (1,1,2,1)
2: (2) 20: (2,3) 30: (1,1,1,2)
3: (1,1) 15: (1,1,1,1) 36: (3,3)
4: (3) 64: (7) 65: (6,1)
5: (2,1) 21: (2,2,1) 96: (1,6)
6: (1,2) 22: (2,1,2) 42: (2,2,2)
8: (4) 26: (1,2,2) 35: (4,1,1)
7: (1,1,1) 128: (8) 49: (1,4,1)
10: (2,2) 19: (3,1,1) 56: (1,1,4)
9: (3,1) 25: (1,3,1) 512: (10)
12: (1,3) 28: (1,1,3) 37: (3,2,1)
16: (5) 34: (4,2) 38: (3,1,2)
11: (2,1,1) 40: (2,4) 41: (2,3,1)
13: (1,2,1) 33: (5,1) 44: (2,1,3)
14: (1,1,2) 48: (1,5) 50: (1,3,2)
32: (6) 256: (9) 52: (1,2,3)
17: (4,1) 23: (2,1,1,1) 1024: (11)
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
fbi[q_]:=If[q=={}, 0, Total[2^q]/2];
Table[Sort[fbi/@Accumulate/@Permutations[primeMS[n]]], {n, 30}]
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CROSSREFS
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A related triangle for partitions is A215366.
Cf. A000120, A029931, A048793, A056239, A066099, A070939, A112798, A114994, A225620, A228351, A333218, A333219.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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