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A321144 Irregular triangle where T(n,k) is the number of divisors of n whose prime indices sum to k. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..87.

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).

Cf. A000005, A112798, A276024, A301854, A301899.

Sequence in context: A330985 A316867 A127327 * A309048 A086072 A086009

Adjacent sequences:  A321141 A321142 A321143 * A321145 A321146 A321147

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Oct 28 2018

STATUS

approved

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Last modified July 11 15:50 EDT 2020. Contains 335626 sequences. (Running on oeis4.)