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Multiplicative with a(p^e) = p^e if sigma(p^e) is prime, and 1 otherwise.
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%I #8 Mar 29 2019 21:08:26

%S 1,2,1,4,1,2,1,1,9,2,1,4,1,2,1,16,1,18,1,4,1,2,1,1,25,2,1,4,1,2,1,1,1,

%T 2,1,36,1,2,1,1,1,2,1,4,9,2,1,16,1,50,1,4,1,2,1,1,1,2,1,4,1,2,9,64,1,

%U 2,1,4,1,2,1,9,1,2,25,4,1,2,1,16,1,2,1,4,1,2,1,1,1,18,1,4,1,2,1,1,1,2,9,100,1,2,1,1,1

%N Multiplicative with a(p^e) = p^e if sigma(p^e) is prime, and 1 otherwise.

%H Antti Karttunen, <a href="/A324892/b324892.txt">Table of n, a(n) for n = 1..65537</a>

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

%F Multiplicative with a(p^e) = p^e if (p^(1+e) - 1)/(p-1) = 1 + p + p^2 + ... + p^e is prime, and 1 otherwise.

%F a(n) = n / A324894(n).

%e For n = 150 = 2 * 3 * 5^2, sigma(2) = 3 is a prime, sigma(3) = 4 is not prime, and sigma(25) = 31 is a prime, thus a(150) = 2 * 25 = 50.

%o (PARI) A324892(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i,1]^isprime(sigma(f[i,1]^f[i,2])))^f[i,2]); };

%o (PARI) A324892(n) = { my(f=factor(n)); prod(i=1, #f~, if(isprime(((f[i,1]^(1+f[i,2]))-1)/(f[i,1]-1)), f[i,1]^f[i,2], 1)); };

%Y Cf. A000203, A010051, A324894.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Mar 29 2019