A252997 -id:A252997 - cp's OEIS frontend

A254035 Sequence A255412 sorted into ascending order, with duplicates removed.

4800, 28800, 57600, 67200, 86400, 96000, 115200, 142800, 144000, 148800, 153600, 182400, 201600, 211200, 230400, 259200, 288000, 297600, 326400, 345600, 355200, 384000, 403200, 432000, 470400, 489600, 499200, 518400, 528000, 547200, 576000, 614400, 633600, 638400, 662400, 672000, 691200, 720000, 729600

Offset: 1

Naohiro Nomoto, Jan 23 2015

nonn

Numbers n such that n = A000203(j) = A000203(k) and A007947(j) = A007947(k), where j != k.
In other words, numbers n such that sigma(x) = n has at least two distinct solutions, with each x having the same squarefree kernel, where sigma(x) is the sum of divisor function (A000203).
Equally, sequence A000203(A255335(n)) sorted into ascending order, with duplicates removed.

			4800 is the sum of divisors of 1512 and 2058, and rad(1512) = rad(2058) = 42, hence 4800 is in the sequence with j=1512 and k=2058.

Subsequence of A159886.
Cf. A000203 (sum of divisors of n), A007947 (squarefree kernel of n).
Cf. A254791 (a subsequence).
Cf. A252997, A255334, A255335, A255412.

a(n) = A000203(A255334(n)) = A000203(A255335(n)) for n = 1 .. 7. - Antti Karttunen, Apr 05 2015

More terms from Antti Karttunen, Apr 13 2015

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).

Original entry on oeis.org

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

Naohiro Nomoto, Dec 15 2014

nonn

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

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

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

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

Cf. A048138, A152454, A252997.

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 *)

cp's OEIS Frontend

A254035 Sequence A255412 sorted into ascending order, with duplicates removed.

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