A066290 - OEIS

A066290

Numbers m such that DivisorSigma(4*k-2, m) mod m = 0 holds presumably for all k; that is, (4k-2)-power-sums of divisors of m are divisible by m for all k.

1, 10, 60, 65, 130, 150, 260, 780, 1105, 2210, 4420, 8840, 13260, 19720, 20737, 32045, 41474, 55250, 64090, 82948, 103685, 128180, 207370, 207553, 221000, 248844, 256360, 295800, 331500, 352529, 384540, 414740, 415106, 450840, 512720, 705058, 829480, 830212

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..38.

FORMULA

DivisorSigma(4k-2, m)/m is an integer for k = 1, 2, 3, .., 200, ...

EXAMPLE

Tested for each m and k < 200. Proof for several values of k seems not so tedious because the number of divisors of the terms of the sequence is not so large: {1, 4, 12, 4, 8, 12, 12, 24, 8, 16, 24, 32, 48, 32, 4, 16, 8, 32, 32, 12, 8, 48, 16, 8, 64, 24, 64, 96, 96, 8, 96, 24, 16, 96, 80, 16, 32, 24}.

MATHEMATICA

lastSeq = {}; max = 100; While[seq = Reap[For[n = 1, n < 10^6, n++, If[AllTrue[Range[max], Mod[DivisorSigma[4 # - 2, n], n] == 0&], Print[n]; Sow[n]]]][[2, 1]]; seq != lastSeq, lastSeq = seq; max = max + 100; Print["max = ", max]]; seq (* Jean-François Alcover, Oct 02 2016 *)

CROSSREFS

Cf. A066135, A066284, A066289.

Sequence in context: A140890 A055714 A046762 * A065641 A121874 A144560

Adjacent sequences: A066287 A066288 A066289 * A066291 A066292 A066293

KEYWORD

nonn

AUTHOR

Labos Elemer, Dec 12 2001

EXTENSIONS

More terms from Jean-François Alcover, Oct 02 2016

STATUS

approved