A392865 a(n) = n mod A117366(n), where A117366 gives the smallest prime greater than the largest prime dividing n.

1, 2, 3, 1, 5, 1, 7, 2, 4, 3, 11, 2, 13, 3, 1, 1, 17, 3, 19, 6, 10, 9, 23, 4, 4, 9, 2, 6, 29, 2, 31, 2, 7, 15, 2, 1, 37, 15, 5, 5, 41, 9, 43, 5, 3, 17, 47, 3, 5, 1, 13, 1, 53, 4, 3, 1, 11, 27, 59, 4, 61, 25, 8, 1, 14, 1, 67, 11, 11, 4, 71, 2, 73, 33, 5, 7, 12, 10, 79, 3, 1, 39, 83, 7, 9, 39, 25, 10, 89, 6, 6, 5, 19

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Mathematica

a117336[n_]:=NextPrime[FactorInteger[n][[-1, 1]]]; a[n_]:=Mod[n, a117336[n]]; Array[a, 93] (* James C. McMahon, Jan 27 2026 *)

Prog

(PARI)
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A392865(n) = (n%nextprime(1+A006530(n)));

Crossrefs

Cf. A006530, A117366, A392870 (multiplicative inverses), A392871 (positions of 1's).

Cf. A392866 [= a(A276086(n))], A392872 [= a(A122111(n))], A392874 [= a(A005940(1+n))], A392875 [= a(A019565(n))], A392876 [= a(A276076(n))].

Sequence in context: A326584 A166333 A322966 * A173239 A366154 A214055

Adjacent sequences: A392862 A392863 A392864 * A392866 A392867 A392868

Keyword

nonn,easy

Author

Antti Karttunen, Jan 27 2026

Status

approved