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A337557 Number of integers less than n with the same number of odd divisors as n.

%I A337557 #74 Nov 01 2020 01:35:34
%S A337557 0,1,0,2,1,2,3,3,0,4,5,6,7,8,0,4,9,1,10,11,1,12,13,14,2,15,2,16,17,3,
%T A337557 18,5,4,19,5,3,20,21,6,22,23,7,24,25,0,26,27,28,4,5,8,29,30,9,10,31,
%U A337557 11,32,33,12,34,35,1,6,13,14,36,37,15,16,38,6,39,40,2,41,17,18,42,43
%N A337557 Number of integers less than n with the same number of odd divisors as n.
%H A337557 David A. Corneth, <a href="/A337557/b337557.txt">Table of n, a(n) for n = 1..10000</a>
%F A337557 a(n) = |{j < n : A001227(j) = A001227(n)}|.
%e A337557 a(10) = 4 because A001227(10) = 2 and also A001227(3) = A001227(5) = A001227(6) = A001227(7) = 2.
%t A337557 Table[Length[Select[Range[n - 1], Sum[Mod[d, 2], {d, Divisors[#]}] == Sum[Mod[d, 2], {d, Divisors[n]}] &]], {n, 80}]
%o A337557 (PARI) a(n)={my(t=numdiv(n/2^valuation(n, 2))); sum(k=1, n-1, numdiv(k/2^valuation(k, 2))==t)} \\ _Andrew Howroyd_, Oct 31 2020
%o A337557 (PARI) first(n) = { my(m = Map(), res = vector(n)); for(i = 1, n, q = numdiv(i >> valuation(i, 2)); if(mapisdefined(m, q), res[i] = mapget(m, q); mapput(m, q, res[i]+1); , mapput(m, q, 1) ) ); res } \\ _David A. Corneth_, Oct 31 2020
%Y A337557 Cf. A001227, A047983, A334655, A335097.
%K A337557 nonn,easy
%O A337557 1,4
%A A337557 _Ilya Gutkovskiy_, Oct 31 2020