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

0, 1, 0, 3, 0, 3, 0, 7, 0, 5, 0, 9, 0, 7, 10, 15, 0, 9, 0, 15, 0, 11, 0, 21, 0, 13, 0, 21, 0, 15, 0, 31, 0, 17, 28, 27, 0, 19, 0, 35, 0, 21, 0, 33, 30, 23, 0, 45, 0, 25, 0, 39, 0, 27, 0, 49, 0, 29, 0, 45, 0, 31, 0, 63, 0, 33, 0, 51, 0, 63, 0, 63, 0, 37, 50, 57, 66, 39, 0, 75, 0, 41, 0, 63, 0, 43, 0, 77, 0, 75, 0, 69

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, A356168, A356171 (positions of 0's), A356172.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356169(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(n-gcd(n,A003961(k)))));

Formula

a(n) = n - A356168(n) = n - gcd(n, A003961(A356164(n))).