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

1,1

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

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

Example

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

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 *)

Crossrefs

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

Cf. A048138, A152454, A252997.

Sequence in context: A185351 A272971 A117948 * A334405 A376997 A386999

Adjacent sequences: A252231 A252232 A252233 * A252235 A252236 A252237

Keyword

nonn

Author

Naohiro Nomoto, Dec 15 2014

Status

approved