A087560 Smallest m > n such that gcd(m, n^2) = n.

2, 6, 6, 12, 10, 30, 14, 24, 18, 30, 22, 60, 26, 42, 30, 48, 34, 90, 38, 60, 42, 66, 46, 120, 50, 78, 54, 84, 58, 210, 62, 96, 66, 102, 70, 180, 74, 114, 78, 120, 82, 210, 86, 132, 90, 138, 94, 240, 98, 150, 102, 156, 106, 270, 110, 168, 114, 174, 118, 420, 122

Offset: 1

Author

Reinhard Zumkeller, Oct 24 2003

Keywords

• nonn

Comments

Equals n multiplied by the least nontrivial number coprime to n. - Amarnath Murthy, Nov 20 2005

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A053669, A062011, A119416, A249270.

Programs

Mathematica

Table[n*Select[Prime[Range[Log2[n] + 1]], ! Divisible[n, #] &][[1]], {n, 61}] (* Ivan Neretin, May 21 2015 *)

PARI

a(n) = forprime(p = 2, , if(n%p, return(n*p))); \\ Amiram Eldar, Feb 01 2025

Formula

a(n) = n*A053669(n).

A000005(a(n)) = 2*A000005(n) = A062011(n). - Reinhard Zumkeller, May 17 2006

Sum_{k=1..n} ~ c * n^2 / 2, where c = A249270. - Amiram Eldar, Feb 01 2025