A373989 a(n) = A276150(gcd(A108951(n), A373158(n))), where A276150 is the digit sum in primorial base, A108951 is fully multiplicative and A373158 is fully additive with a(p) = p# for prime p, where x# is the primorial A034386(x).

1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 2, 2, 4, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 6, 4, 2, 2, 1, 4, 1, 2, 1, 2, 6, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 6, 1, 1, 1, 4, 2, 1, 4, 2, 2, 2, 2, 1, 2, 6, 1, 2, 2, 2, 4, 1, 1, 5, 4, 1, 1, 1, 2, 1

Offset: 1

Author

Antti Karttunen, Jun 26 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A034386, A108951, A276150, A373158, A373985.

Cf. also A324888.

Programs

PARI

A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A373985(n) = { my(f=factor(n),m=1,s=0); for(i=1, #f~, my(x=prod(i=1,primepi(f[i, 1]),prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); gcd(m,s); };
A373989(n) = A276150(A373985(n));

Formula

a(n) = A276150(A373985(n)).