A373140 Numbers k such that A276085(k) is a multiple of 5, where A276085 is the primorial base log-function.

1, 7, 11, 13, 17, 18, 19, 23, 24, 29, 31, 32, 37, 41, 43, 45, 47, 49, 53, 59, 60, 61, 67, 71, 73, 77, 79, 80, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 126, 127, 131, 133, 137, 139, 143, 149, 150, 151, 157, 161, 163, 167, 168, 169, 173, 179, 181, 187, 191, 193, 197, 198, 199, 200, 203, 209, 211, 217, 221

Offset: 1

Author

Antti Karttunen, May 26 2024

Keywords

• nonn

Comments

Because A276085 is completely additive, this is a multiplicative semigroup; if m and n are in the sequence then so is m*n.

This looks likely to be the integers in the multiplicative subgroup of the positive rationals generated by 32, 24, 80 and primes greater than 5. - Peter Munn, Jul 15 2024

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A276085, A373139 (characteristic function).

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A373139(n) = !(A276085(n)%5);