A324894 Multiplicative with a(p^e) = p^e if sigma(p^e) is composite, and 1 otherwise.

1, 1, 3, 1, 5, 3, 7, 8, 1, 5, 11, 3, 13, 7, 15, 1, 17, 1, 19, 5, 21, 11, 23, 24, 1, 13, 27, 7, 29, 15, 31, 32, 33, 17, 35, 1, 37, 19, 39, 40, 41, 21, 43, 11, 5, 23, 47, 3, 49, 1, 51, 13, 53, 27, 55, 56, 57, 29, 59, 15, 61, 31, 7, 1, 65, 33, 67, 17, 69, 35, 71, 8, 73, 37, 3, 19, 77, 39, 79, 5, 81, 41, 83, 21, 85, 43, 87, 88, 89, 5, 91

Offset: 1

Author

Antti Karttunen, Mar 29 2019

Keywords

• nonn
• mult

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A010051, A324892.

Programs

PARI

A324894(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i,1]^!isprime(sigma(f[i,1]^f[i,2])))^f[i,2]); };

Formula

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

a(n) = n / A324892(n).