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A211347 Numbers n such that n = sigma_k(m) for some k >= 1. 3
1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 24, 26, 28, 30, 31, 32, 33, 36, 38, 39, 40, 42, 44, 48, 50, 54, 56, 57, 60, 62, 63, 65, 68, 72, 73, 74, 78, 80, 82, 84, 85, 90, 91, 93, 96, 98, 102, 104, 108, 110, 112, 114, 120, 121, 122 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sigma_k(n) = Sum[d|n, d^k].

Sigma_0(n) can be any positive integer and so is ignored in this sequence.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

Eric W. Weisstein, MathWorld: Divisor function

EXAMPLE

Sigma_2(4) = 1 + 4 + 16 = 21 so 21 is in the sequence.

MATHEMATICA

upto[n_] := Select[Union@Flatten[{1, DivisorSigma[Range@Max[1, Floor@Log[#, n]], #] & /@ Range[2, n]}], # <= n &]; upto[122] (* Giovanni Resta, Feb 05 2013 *)

CROSSREFS

Cf. A000203, A001157, A001158, A001159, A001160.

Cf. A013954, A013955, A013956, A013957, A013958, A013959, A013960, A013961, A013962, A013963, A013964, A013965, A013966, A013967, A013968, A013969, A013970, A013971, A013972.

Cf. A000005.

Sequence in context: A048135 A026500 A091213 * A258777 A298004 A039238

Adjacent sequences:  A211344 A211345 A211346 * A211348 A211349 A211350

KEYWORD

nonn

AUTHOR

Jon Perry, Feb 05 2013

STATUS

approved

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Last modified February 24 11:06 EST 2018. Contains 299603 sequences. (Running on oeis4.)