A337204 - OEIS

%I #8 Aug 28 2020 11:06:52

%S 1,1,4,1,24,4,192,1,13,24,2304,4,32256,192,78,1,580608,13,11612160,24,

%T 624,2304,278691840,4,403,32256,40,192,8360755200,78,267544166400,1,

%U 7488,580608,3224,13,10166678323200,11612160,104832,24,427000489574400,624,18788021541273600,2304,240,278691840,901825033981132800,4,22971,403

%N Sum of the odd divisors of the primorial inflation of n.

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A000593(A108951(n)).

%t Array[DivisorSum[Apply[Times, FactorInteger[#] /. {p_, e_} /; e > 0 :> Apply[Times, Prime@ Range@ PrimePi@ p]^e], # &, OddQ] &, 50] (* _Michael De Vlieger_, Aug 27 2020 *)

%o (PARI)

%o A000593(n) = sigma(n>>valuation(n, 2));

%o A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951

%o A337204(n) = A000593(A108951(n));

%Y Row 1 of A337205.

%Y Cf. A000593, A034386, A108951, A337203.

%Y Cf. also A322819.

%K nonn

%O 1,3

%A _Antti Karttunen_, Aug 22 2020