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A321144
Irregular triangle where T(n,k) is the number of divisors of n whose prime indices sum to k.
3
1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0
OFFSET
1,45
COMMENTS
The rows are all palindromes.
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.
EXAMPLE
Triangle begins:
1
1 1
1 0 1
1 1 1
1 0 0 1
1 1 1 1
1 0 0 0 1
1 1 1 1
1 0 1 0 1
1 1 0 1 1
1 0 0 0 0 1
1 1 2 1 1
1 0 0 0 0 0 1
1 1 0 0 1 1
1 0 1 1 0 1
1 1 1 1 1
1 0 0 0 0 0 0 1
1 1 1 1 1 1
1 0 0 0 0 0 0 0 1
1 1 1 1 1 1
1 0 1 0 1 0 1
1 1 0 0 0 1 1
1 0 0 0 0 0 0 0 0 1
1 1 2 2 1 1
1 0 0 1 0 0 1
1 1 0 0 0 0 1 1
1 0 1 0 1 0 1
1 1 1 0 1 1 1
1 0 0 0 0 0 0 0 0 0 1
1 1 1 2 1 1 1
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]
Table[Count[Total/@primeMS/@Divisors[n], k], {n, 20}, {k, 0, Total[primeMS[n]]}]
CROSSREFS
Row lengths are A056239. Number of nonzero entries in row n is A299701(n).
Sequence in context: A377080 A316867 A127327 * A309048 A086072 A086009
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Oct 28 2018
STATUS
approved