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a(n) = A038040(A225546(n)).
3

%I #12 Jul 09 2020 22:39:15

%S 1,4,12,6,80,32,2304,24,27,192,1114112,72,141733920768,5120,448,10,

%T 1199038364791120855040,108,43896425332801061786775324358698099277824,

%U 480,11264,2359296,29758566933990262223857743147232792318290386059069624958140599090033674317463552,192,405,292057776128,324,13824

%N a(n) = A038040(A225546(n)).

%C Question: Is it possible for a(n)/A331733(n) to be an integer when n is a square > 1? This is equivalent to the question whether there are odd Harmonic numbers (A001599) larger than one.

%F a(n) = A225546(n) * A331309(n).

%t Array[# DivisorSigma[0, #] &@ If[# == 1, 1, Times @@ Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]] &, 28] (* _Michael De Vlieger_, Jul 08 2020 *)

%o (PARI)

%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

%o A335914(n) = if(1==n,1,my(f=factor(n),u=#binary(vecmax(f[, 2])),prods=vector(u,x,1),m=1,e); for(i=1,u,for(k=1,#f~, if(bitand(f[k,2],m),prods[i] *= f[k,1])); m<<=1); prod(i=1,u,(1+A048675(prods[i]))*(prime(i)^A048675(prods[i]))));

%Y Cf. A001599, A038040, A225546, A331309.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 08 2020