A356168 Greatest common divisor of n and A003961(A356164(n)), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 5, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1, 33, 17, 7, 9, 37, 19, 39, 5, 41, 21, 43, 11, 15, 23, 47, 3, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 1, 65, 33, 67, 17, 69, 7, 71, 9, 73, 37, 25, 19, 11, 39, 79, 5, 81, 41, 83, 21, 85, 43

Offset: 1

Author

Antti Karttunen, Jul 28 2022

Keywords

• nonn

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, A356164, A356166, A356167, A356169.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356168(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(gcd(n,A003961(k)))));

Formula

a(n) = gcd(n, A003961(A356164(n))).

a(n) = gcd(n, A356169(n)) = n - A356169(n).