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A332306
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a(n) is the least k such that A121663(k) = n.
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1
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0, 1, 2, 4, 8, 3, 32, 5, 128, 9, 512, 6, 2048, 33, 10, 65, 32768, 18, 131072, 12, 34, 513, 2097152, 7, 8388608, 2049, 130, 36, 134217728, 11, 536870912, 68, 514, 32769, 40, 19, 34359738368, 131073, 2050, 13, 549755813888, 35, 2199023255552, 516, 136, 2097153
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OFFSET
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1,3
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COMMENTS
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The binary representation of a(n) encodes the colexicographically earliest factorization of n into distinct factors greater than 1.
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LINKS
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FORMULA
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a(n) = 2^(n-2) iff n is a prime number of the square of a prime number (A000430).
a(n!) = 2^(n-1)-1 for any n > 0.
a(p_1*...*p_k) = 2^(p_1-2)+...+2^(p_k-2) for distinct primes numbers p_1, ..., p_k.
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EXAMPLE
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The first terms, alongside their binary representations and factorizations, are:
n a(n) bin(a(n)) Factorization
-- ------ ------------------ -------------
1 0 0
2 1 1 2
3 2 10 3
4 4 100 4
5 8 1000 5
6 3 11 2*3
7 32 100000 7
8 5 101 2*4
9 128 10000000 9
10 9 1001 2*5
11 512 1000000000 11
12 6 110 3*4
13 2048 100000000000 13
14 33 100001 2*7
15 10 1010 3*5
16 65 1000001 2*8
17 32768 1000000000000000 17
18 18 10010 3*6
19 131072 100000000000000000 19
20 12 1100 4*5
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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