|
|
A358172
|
|
Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (z-a+1, z-b+1, ..., z-y+1).
|
|
6
|
|
|
1, 2, 1, 1, 1, 3, 2, 2, 4, 2, 1, 1, 1, 2, 1, 3, 3, 3, 5, 2, 2, 2, 1, 6, 1, 1, 4, 4, 3, 2, 1, 1, 1, 1, 4, 7, 2, 2, 2, 1, 8, 5, 3, 3, 3, 4, 3, 5, 5, 2, 2, 9, 2, 2, 2, 2, 1, 3, 1, 6, 6, 6, 2, 1, 1, 3, 4, 4, 4, 7, 10, 3, 3, 2, 11, 3, 3, 1, 1, 1, 1, 1, 4, 5, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1: .
2: .
3: .
4: 1
5: .
6: 2
7: .
8: 1 1
9: 1
10: 3
11: .
12: 2 2
13: .
14: 4
15: 2
16: 1 1 1
17: .
18: 2 1
19: .
20: 3 3
For example, the prime indices of 900 are (1,1,2,2,3,3), so row 900 is 3 - (1,1,2,2,3) + 1 = (3,3,2,2,1).
|
|
MATHEMATICA
|
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, {}, 1+Last[primeMS[n]]-Most[primeMS[n]]], {n, 100}]
|
|
CROSSREFS
|
Even-indexed rows have sums A243503.
A243055 subtracts the least prime index from the greatest.
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|