A338572 - OEIS

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

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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}]