A338572 Number of integers less than n with the same number of factorizations into prime powers as n.

0, 1, 2, 0, 3, 4, 5, 0, 1, 6, 7, 2, 8, 9, 10, 0, 11, 3, 12, 4, 13, 14, 15, 1, 5, 16, 2, 6, 17, 18, 19, 0, 20, 21, 22, 0, 23, 24, 25, 3, 26, 27, 28, 7, 8, 29, 30, 1, 9, 10, 31, 11, 32, 4, 33, 5, 34, 35, 36, 12, 37, 38, 13, 0, 39, 40, 41, 14, 42, 43, 44, 0, 45, 46, 15, 16, 47, 48, 49, 2

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Eric Weisstein's World of Mathematics, Abelian Group

Formula

a(n) = |{j < n : A000688(j) = A000688(n)}|.

Example

a(18) = 3 because A000688(18) = 2 and also A000688(4) = A000688(9) = A000688(12) = 2.

Mathematica

Table[Length[Select[Range[n - 1], FiniteAbelianGroupCount[#] == FiniteAbelianGroupCount[n] &]], {n, 80}]

Prog

(PARI) nf(n) = my(f=factor(n)[, 2]); prod(i=1, #f, numbpart(f[i])); \\ A000688
a(n) = my(nb=nf(n)); sum(k=1, n-1, nf(k) == nb); \\ Michel Marcus, Nov 03 2020

Crossrefs

Cf. A000688, A338568, A338569.

Sequence in context: A087819 A290820 A278029 * A066246 A198370 A173517

Adjacent sequences: A338569 A338570 A338571 * A338573 A338574 A338575

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 03 2020

Status

approved