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The sum of divisors of n that are terms of A056166.
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%I #8 Nov 02 2023 10:26:59

%S 1,1,1,5,1,1,1,13,10,1,1,5,1,1,1,13,1,10,1,5,1,1,1,13,26,1,37,5,1,1,1,

%T 45,1,1,1,50,1,1,1,13,1,1,1,5,10,1,1,13,50,26,1,5,1,37,1,13,1,1,1,5,1,

%U 1,10,45,1,1,1,5,1,1,1,130,1,1,26,5,1,1,1,13

%N The sum of divisors of n that are terms of A056166.

%C The number of these divisors is A095691(n) and the largest of them is A366993(n).

%H Amiram Eldar, <a href="/A366990/b366990.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = 1 + Sum_{primes q <= e} p^q.

%F a(n) >= 1, with equality if and only if n is squarefree (A005117).

%t f[p_, e_] := 1 + Total[p^Select[Range[e], PrimeQ]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(j = 1, f[i, 2], if(isprime(j), f[i, 1]^j)));}

%Y Cf. A005117, A056166, A095691, A366988, A366993.

%K nonn,easy,mult

%O 1,4

%A _Amiram Eldar_, Oct 31 2023