A392870 Multiplicative inverse of {n mod A117366(n)} in finite field F(A117366(n)), where A117366 gives the smallest prime greater than the largest prime dividing n.

1, 2, 2, 1, 3, 1, 8, 2, 4, 5, 6, 3, 4, 4, 1, 1, 9, 2, 17, 6, 10, 3, 24, 4, 2, 2, 3, 2, 15, 4, 6, 2, 2, 14, 6, 1, 10, 20, 7, 3, 21, 5, 35, 8, 5, 12, 44, 2, 9, 1, 3, 1, 49, 4, 9, 1, 21, 23, 30, 2, 11, 3, 7, 1, 11, 1, 53, 7, 8, 3, 36, 3, 13, 5, 3, 10, 12, 12, 62, 5, 1, 32, 74, 8, 17, 41, 5, 4, 12, 6, 3, 6, 2, 22, 8

Offset

1,2

Links

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

Example

For n = 5, itself a prime, the next larger prime is 7, so 5 mod 7 = 5, whose inverse in F(7) is 3 as 3*5 = 15 == 1 (mod 7), thus a(5) = 3.
For n = 14 = 2*7, the next larger prime is 11, so 14 mod 11 = 3, whose inverse in F(11) is 4, as 3*4 = 12 == 1 (mod 11), thus a(14) = 4.
For n = 15 = 3*5, the next larger prime is 7, so 15 mod 7 = 1, whose inverse in F(11) (like in any field) is 1, thus a(15) = 1.

Prog

(PARI)
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A392870(n) = lift(Mod(1/n, nextprime(1+A006530(n))));

Crossrefs

Cf. A006530, A069830 [= a(prime(n))], A117366, A392865 (multiplicative inverses), A392871 (positions of 1's).

Sequence in context: A069004 A381495 A182490 * A053274 A243926 A281013

Adjacent sequences: A392867 A392868 A392869 * A392871 A392872 A392873

Keyword

nonn,easy

Author

Antti Karttunen, Jan 27 2026

Status

approved