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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.)