

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).


1



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
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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 A242344 A247111
Adjacent sequences: A252231 A252232 A252233 * A252235 A252236 A252237


KEYWORD

nonn


AUTHOR

Naohiro Nomoto, Dec 15 2014


STATUS

approved



