A331283 a(n) = gcd(n, A329605(n)), where A329605(n) gives the number of divisors of primorial inflation of n, A108951(n).

1, 2, 1, 1, 1, 6, 1, 4, 9, 2, 1, 4, 1, 2, 3, 1, 1, 6, 1, 4, 3, 2, 1, 2, 1, 2, 1, 4, 1, 6, 1, 2, 3, 2, 1, 3, 1, 2, 3, 20, 1, 6, 1, 4, 1, 2, 1, 12, 1, 2, 3, 4, 1, 2, 1, 8, 3, 2, 1, 30, 1, 2, 1, 1, 1, 6, 1, 4, 3, 2, 1, 18, 1, 2, 3, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 3, 8, 1, 10, 1, 4, 3, 2, 1, 2, 1, 2, 1, 5, 1, 6, 1, 8, 3

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..11025

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial numbers

Formula

a(n) = gcd(n, A329605(n)).

a(A002110(n)) = gcd(A002110(n), A000142(1+n)) = A034386(1+n), for n >= 0.

Prog

(PARI) A331283(n) = if(1==n, 1, my(f=factor(n), e=1, m=1); forstep(i=#f~, 1, -1, e += f[i, 2]; m *= e^(primepi(f[i, 1])-if(1==i, 0, primepi(f[i-1, 1])))); gcd(n, m));

Crossrefs

Cf. A000142, A002110, A034386, A108951, A329605.

Cf. also A009191, A329612.

Sequence in context: A292977 A295381 A351420 * A060185 A348091 A129110

Adjacent sequences: A331280 A331281 A331282 * A331284 A331285 A331286

Keyword

nonn

Author

Antti Karttunen, Jan 14 2020

Status

approved