cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A193335 Number of odd divisors of sigma(n).

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%I A193335 #23 Jul 06 2022 06:58:50
%S A193335 1,2,1,2,2,2,1,4,2,3,2,2,2,2,2,2,3,4,2,4,1,3,2,4,2,4,2,2,4,3,1,6,2,4,
%T A193335 2,4,2,4,2,6,4,2,2,4,4,3,2,2,4,4,3,3,4,4,3,4,2,6,4,4,2,2,2,2,4,3,2,6,
%U A193335 2,3,3,8,2,4,2,4,2,4,2,4
%N A193335 Number of odd divisors of sigma(n).
%H A193335 Charles R Greathouse IV, <a href="/A193335/b193335.txt">Table of n, a(n) for n = 1..10000</a>
%F A193335 a(n) = A001227(A000203(n)). - _Michel Marcus_, Jan 14 2014
%e A193335 a(8) = 4 because sigma(8) = 15 and the 4 odd divisors are { 1, 3, 5, 15}.
%t A193335 f[n_] := Block[{d = Divisors[DivisorSigma[1,n]]}, Count[OddQ[d], True]]; Table[f[n], {n, 80}]
%t A193335 Table[Count[Divisors[DivisorSigma[1,n]],_?OddQ],{n,80}] (* _Harvey P. Dale_, Jul 06 2019 *)
%t A193335 odd[n_] := DivisorSigma[0, n / 2^IntegerExponent[n, 2]]; a[n_] := odd[DivisorSigma[1, n]]; Array[a, 100] (* _Amiram Eldar_, Jul 06 2022 *)
%o A193335 (PARI) a(n)=sumdiv(sigma(n,1),d,d%2);
%o A193335 (PARI) a(n)=n=sigma(n);numdiv(n>>valuation(n,2)) \\ _Charles R Greathouse IV_, Jul 30 2011
%Y A193335 Cf. A000203 (sigma), A001227.
%K A193335 nonn
%O A193335 1,2
%A A193335 _Michel Lagneau_, Jul 23 2011