A328098 If A327928(n) is zero, a(n) = A003415(n), otherwise a(n) = A327858(n) = gcd(A003415(n), A276086(n)).

0, 1, 1, 1, 1, 5, 1, 1, 6, 7, 1, 1, 1, 9, 1, 1, 1, 21, 1, 1, 10, 13, 1, 1, 10, 15, 3, 1, 1, 31, 1, 5, 14, 19, 1, 1, 1, 21, 1, 1, 1, 41, 1, 1, 39, 25, 1, 7, 14, 45, 5, 7, 1, 3, 1, 1, 22, 31, 1, 1, 1, 33, 51, 1, 18, 61, 1, 1, 26, 59, 1, 1, 1, 39, 55, 5, 18, 71, 1, 1, 1, 43, 1, 1, 22, 45, 1, 35, 1, 123, 5, 1, 34, 49, 1, 1, 1, 77, 75, 35, 1, 91, 1, 1, 71

Offset: 1

Author

Antti Karttunen, Oct 07 2019

Keywords

• nonn

Comments

After zero, sequence contains only terms of A048103.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A328097, A328099.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
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; };
A328098(n) = if(1==n,0,my(u=A003415(n)); if(!A129251(u),u,gcd(u,A276086(u))));