A356166 Greatest common divisor of n and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 3, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 32, 1, 2, 5, 4, 1, 2, 1, 8, 1, 2, 1, 4, 3, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 12, 1, 2, 1, 64, 1, 2, 1, 4, 1, 10, 1, 8, 1, 2, 3, 4, 7, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 6, 1, 4, 1, 2, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8, 5

Offset: 1

Author

Antti Karttunen, Jul 28 2022

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A191002, A356164, A356165, A356167, A356168, A356171 (positions of 1's), A356172.

Cf. also A345992, A356151.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356166(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(gcd(n,k))));

Formula

a(n) = gcd(n, A356164(n)) = gcd(n, A356165(n)) = gcd(A356164(n), A356165(n)).