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%I #8 Nov 03 2020 11:36:56
%S 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,
%T 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,
%U 34,35,36,12,37,38,13,0,39,40,41,14,42,43,44,0,45,46,15,16,47,48,49,2
%N Number of integers less than n with the same number of factorizations into prime powers as n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbelianGroup.html">Abelian Group</a>
%F a(n) = |{j < n : A000688(j) = A000688(n)}|.
%e a(18) = 3 because A000688(18) = 2 and also A000688(4) = A000688(9) = A000688(12) = 2.
%t Table[Length[Select[Range[n - 1], FiniteAbelianGroupCount[#] == FiniteAbelianGroupCount[n] &]], {n, 80}]
%o (PARI) nf(n) = my(f=factor(n)[, 2]); prod(i=1, #f, numbpart(f[i])); \\ A000688
%o a(n) = my(nb=nf(n)); sum(k=1, n-1, nf(k) == nb); \\ _Michel Marcus_, Nov 03 2020
%Y Cf. A000688, A338568, A338569.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Nov 03 2020