A356165 a(n) = n minus the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

0, 0, 1, 0, 2, 4, 2, 0, 5, 4, 4, 8, 2, 4, 12, 0, 4, 14, 2, 8, 11, 8, 4, 16, 16, 4, 19, 8, 6, 24, 2, 0, 19, 8, 30, 32, 6, 4, 17, 16, 4, 32, 2, 16, 39, 8, 4, 32, 24, 32, 25, 8, 6, 46, 34, 16, 23, 12, 6, 48, 2, 4, 43, 0, 32, 52, 6, 16, 31, 60, 4, 64, 2, 12, 66, 8, 70, 56, 6, 32, 65, 8, 4, 64, 46, 4, 41, 32, 6, 84, 36

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. A000079 (positions of zeros), A000720, A001223, A003961, A191002, A356164, A356166.

Cf. also A355945.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356165(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(n-k)));

Formula

a(n) = n - A356164(n).

For all odd primes p, a(p) = A001223(A000720(p)-1).