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 A076617 Numbers k such that sum of the divisors d of k divides 1 + 2 + ... + k = k(k+1)/2. 5
 1, 2, 15, 20, 24, 95, 104, 207, 224, 287, 464, 1023, 1199, 1952, 4095, 4607, 8036, 12095, 15872, 16895, 19359, 22932, 23519, 28799, 45440, 45695, 54144, 77375, 101567, 102024, 130304, 159599, 163295, 223199, 296207, 317184, 352799, 522752, 524160, 635904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Alternately, numbers k such that sum of the divisors d of k divides the sum of the non-divisors d' of k, where 1 <= d, d' <= k. Numbers k such that A232324(k) = antisigma(k) mod sigma(k) = A024816(n) mod A000203(n) = 0. - Jaroslav Krizek, Jan 24 2014 LINKS Donovan Johnson, Table of n, a(n) for n = 1..200 FORMULA a(n+2) = A066860(n) - Alex Ratushnyak, Jul 02 2013 EXAMPLE The sum of the divisors of 15 is sigma(15) = 24; the sum of the non-divisors of 15 that are between 1 and 15 is 2 + 4 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 = 96. Since 24 divides 96, 15 is a term of the sequence. MAPLE with(numtheory); P:=proc(i) local a, n; for n from 1 to i do   a:=(n*(n+1))/(2*sigma(n))-1; if a=trunc(a) then print(n); fi; od; end: P(10000000000); # Paolo P. Lava, Dec 12 2011 MATHEMATICA a = {}; Do[ s = DivisorSigma[1, i]; n = (i (i + 1) / 2) - s; If[Mod[n, s] == 0, a = Append[a, i]], {i, 1, 10^5}]; a Select[Range, Divisible[(#(#+1))/2, DivisorSigma[1, #]]&] (* Harvey P. Dale, Aug 01 2019 *) PROG (PARI) is(n)=n*(n+1)/2%sigma(n)==0 \\ Charles R Greathouse IV, May 02 2013 CROSSREFS Cf. A000203, A024816, A066860. Sequence in context: A031022 A194542 A076646 * A091791 A281660 A244324 Adjacent sequences:  A076614 A076615 A076616 * A076618 A076619 A076620 KEYWORD nonn AUTHOR Joseph L. Pe, Oct 22 2002 EXTENSIONS New name from J. M. Bergot, May 02 2013 More terms from T. D. Noe, May 02 2013 STATUS approved

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Last modified May 29 15:44 EDT 2020. Contains 334704 sequences. (Running on oeis4.)