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%I #9 Feb 04 2023 14:14:40
%S 1,1,4,1,6,4,1,1,13,6,12,4,1,1,24,1,18,13,1,6,4,12,1,4,31,1,40,1,1,24,
%T 32,1,48,18,6,13,1,1,4,6,42,4,1,12,78,1,1,4,1,31,72,1,1,40,72,1,4,1,
%U 60,24,1,32,13,1,6,48,68,18,4,6,1,13,1,1,124,1,12
%N a(n) is the sum of divisors of n that have only prime-indexed prime factors.
%C Equivalently, a(n) is the sum of divisors of the largest divisor of n that has only prime-indexed prime factors.
%H Amiram Eldar, <a href="/A360327/b360327.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 1 if and only if n is in A320628.
%F a(n) = A000203(n) if and only if n is in A076610.
%F a(n) = A000203(A360325(n)).
%F Multiplicative with a(p^e) = (p^(e+1)-1)/(p-1) if p is a prime-indexed prime (A006450), and 1 otherwise.
%t f[p_, e_] := If[PrimeQ[PrimePi[p]], (p^(e+1)-1)/(p-1), 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) a(n) = {my(f = factor(n), p = f[,1], e = f[,2]); prod(i = 1, #p, if(isprime(primepi(p[i])), (p[i]^(e[i]+1)-1)/(p[i]-1), 1));}
%Y Cf. A000203, A006450, A076610, A320628, A360325, A360326.
%K nonn,mult
%O 1,3
%A _Amiram Eldar_, Feb 03 2023
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