A324534 The smallest common prime factor of sigma(n) and A276086(n), or 1 if no such prime exists.

1, 3, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 5, 1, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 1, 3, 2, 7, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 5, 2, 3, 2, 5, 2, 7, 2, 3, 1, 3, 2, 7, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 7, 2, 3, 2, 7, 2, 1, 2, 3, 2

Offset: 1

Author

Antti Karttunen, Mar 11 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A020639, A276086, A324644.

Programs

PARI

A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A324534(n) = A020639(gcd(sigma(n),A276086(n)));

Formula

a(n) = A020639(A324644(n)) = A020639(gcd(A000203(n),A276086(n))).