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A211347 Numbers n such that n = sigma_k(m) for some k >= 1. 5
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.

The asymptotic density of this sequence is 0 (Niven, 1951, Rao and Murty, 1979). - Amiram Eldar, Jul 23 2020

LINKS

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

Ivan Niven, The asymptotic density of sequences, Bull. Amer. Math. Soc., Vol. 57 (1951), pp. 420-434.

R. Sita Rama Chandra Rao and G. Sri Rama Chandra Murty, On a theorem of Niven, Canadian Mathematical Bulletin, Vol 22, No. 1 (1979), pp. 113-115.

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 *)

PROG

(PARI) list(lim)=if(lim<3, return(if(lim<1, [], [1]))); my(v=List([1])); for(k=1, logint((lim\=1)-1, 2), forfactored(m=2, sqrtnint(lim-1, k), my(t=sigma(m, k)); if(t<=lim, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Apr 09 2022

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: A304812 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 May 19 13:24 EDT 2022. Contains 353833 sequences. (Running on oeis4.)