A252234 Numbers n such that there exists an m so that squarefree kernel of n = squarefree kernel of m, and n is the sum of the proper divisors of m (m may equal n).

6, 28, 36, 50, 240, 312, 384, 450, 496, 810, 1008, 1344, 4256, 4536, 8128, 10800, 11700, 14112, 15288, 19656, 23040, 49686, 90720, 95040, 98280, 98553, 124848, 129024, 153760, 249018, 256932, 260100, 378225, 404586, 454860, 532224, 561834, 700245, 714240

Offset: 1

Author

Naohiro Nomoto, Dec 15 2014

Keywords

• nonn

Comments

Since m=n is allowed, perfect numbers (A000396) are terms of this sequence. - Michel Marcus, Jan 02 2015

m: 6, 24, 28, 40, 120, 216, 234, 270, 360, 496, 588, 672, 2016, ..., . - Robert G. Wilson v, Feb 28 2015

Odd members are 98553, 378225, 700245, ..., . - Robert G. Wilson v, Feb 28 2015

Examples

			For n = 36, m = 24, 36 is the sum of the proper divisors of 24, and rad(36) = rad(24) = 6.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..157
• Robert G. Wilson v, Table of n, a(n) and m for n = 1..157

Crossrefs

Cf. A001065 (sum of proper divisors of n), A007947 (the squarefree kernel of n).

Cf. A048138, A152454, A252997.

Programs

Mathematica

rad[n_] := Times @@ (First@ # & /@ FactorInteger@ n); f[n_] := Block[{sd = DivisorSigma[1, n] - n}, If[ rad[n] == rad[sd], sd, 0]]; k = 1; lst = {}; While[k < 1000001, a = f@ k; If[a > 0, AppendTo[lst, a]]; k++]; Sort@ lst (* Robert G. Wilson v, Feb 28 2015 *)