A355945 a(n) = n minus the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.

0, 1, 1, 0, 0, 4, 0, 0, 6, 5, 0, 8, 0, 7, 10, 0, 0, 15, 0, 12, 7, 11, 0, 16, 15, 13, 18, 0, 0, 25, 0, 0, 22, 17, 28, 32, 0, 19, 13, 32, 0, 28, 0, 0, 40, 23, 0, 32, 14, 40, 34, 0, 0, 45, 44, 24, 19, 29, 0, 52, 0, 31, 42, 0, 52, 55, 0, 0, 46, 63, 0, 56, 0, 37, 65, 0, 44, 52, 0, 64, 54, 41, 0, 56, 68, 43, 58, 0, 0, 85, 52

Offset: 1

Author

Antti Karttunen, Jul 27 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A276086, A324580, A355944, A356151, A356160 (positions of zeros), A356161.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355945(n) = for(k=1, oo, if((k*A276086(k))%n==0, return(n-k)));

Formula

a(n) = n - A355944(n).