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Sum of odd divisors of sopf(n).
1

%I #13 May 18 2023 08:35:09

%S 0,1,4,1,6,6,8,1,4,8,12,6,14,13,1,1,18,6,20,8,6,14,24,6,6,24,4,13,30,

%T 6,32,1,8,20,4,6,38,32,1,8,42,4,44,14,1,31,48,6,8,8,6,24,54,6,1,13,12,

%U 32,60,6,62,48,6,1,13,1,68,20,14,8,72,6,74,56,1

%N Sum of odd divisors of sopf(n).

%H Amiram Eldar, <a href="/A193529/b193529.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000593(A008472(n)). - _Amiram Eldar_, May 18 2023

%e a(5) = 6 because sopf(5) = 5, and the sum of the 2 odd divisors of 5, {1, 5}, is 6.

%t Table[Total[Select[Divisors[Plus@@First[Transpose[FactorInteger[n]]]], OddQ[#]&]], {n, 100}]

%t sopf[n_] := Total[FactorInteger[n][[;;, 1]]]; oddsigma[n_] := DivisorSigma[1, n/2^IntegerExponent[n, 2]]; a[1] = 0; a[n_] := oddsigma[sopf[n]]; Array[a, 100] (* _Amiram Eldar_, May 18 2023 *)

%Y Cf. A000593, A008472 (sopf), A193523.

%K nonn

%O 1,3

%A _Michel Lagneau_, Jul 29 2011