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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).
3
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
1,4
FORMULA
a(n) = A276150(A373985(n)).
PROG
(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); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 26 2024
STATUS
approved