A318660 Remainder when A064988(n) is divided by n.

0, 1, 2, 1, 1, 3, 3, 3, 7, 3, 9, 9, 2, 9, 10, 1, 8, 3, 10, 19, 1, 5, 14, 15, 21, 19, 17, 13, 22, 15, 3, 19, 23, 7, 12, 9, 9, 11, 10, 17, 15, 3, 19, 15, 5, 19, 23, 21, 44, 13, 40, 5, 29, 51, 11, 11, 50, 37, 41, 15, 39, 9, 47, 25, 61, 3, 63, 55, 1, 1, 69, 27, 2, 27, 5, 71, 65, 69, 6, 11, 58, 45, 16, 9, 54, 57, 23, 45, 16, 15, 60, 11, 77, 69

Offset: 1

Author

Altug Alkan and Antti Karttunen, Sep 08 2018

Keywords

• nonn

Comments

Inspired by A064988 and a 'minimum' version of it (A318871).

a(n) = 0 only for n = 1. Numbers n such that a(n) = 1 are 2, 4, 5, 16, 21, 69, 70, 181, 265, 370, 1043, 3760, 4531, ...

Examples

			a(6) = prime(2)*prime(3) mod 6 = 15 mod 6 = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A064988, A076240, A318668, A318871.

Programs

Mathematica

Table[Mod[If[n == 1, 1, Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 1 :> Prime[p]^e]], n], {n, 94}] (* Michael De Vlieger, Sep 10 2018 *)

PARI

A318660(n) = { my(f = factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1]); ); (factorback(f)%n); }; \\ After code in A064988.

Formula

a(n) = A064988(n) mod n.

a(A000040(n)) = A076240(n).