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 A134382 a(n) is the smallest number k larger than a(n-1) such that n*d(k)*sopf(k)=sigma(k), where d is the number of divisors (A000005) and sopf the sum of prime factors without repetition (A008472). 8
 20, 140, 464, 660, 1276, 1365, 2204, 2508, 2805, 2907, 5590, 5698, 5742, 6006, 7395, 8680, 14645, 15052, 18875, 19170, 19740, 23871, 34579, 34804, 35164, 35244, 35934, 38121, 106805, 114953, 261536, 503082 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence suggested by Puzzle 419 in Carlos Rivera's The Prime Puzzles & Problems Connection. Subsequence of A070222. - R. J. Mathar, Feb 05 2010 For n=33, the search for terms k that satisfy 33*d(k)*sopf(k)=sigma(k), without being greater than a(32), gives 21070, 25585, 30702, 36120, 41710, 49256, 52269, 68906, 74692, 92785, 95702, 111342, 117626, 383086 with no other terms up to 10^9. So this sequence might well be complete. - Michel Marcus, Oct 02 2019 a(33) > 9*10^12, if it exists. - Giovanni Resta, Oct 03 2019 LINKS Carlos Rivera, Puzzle 419. Four SOPF questions, Prime Puzzles. FORMULA a(n) > a(n-1): n*A000005(a(n))*A008472(a(n)) = A000203(a(n)). - R. J. Mathar, Nov 16 2007, Jun 24 2009 MAPLE A008472 := proc(n) local divs, i ; if n = 1 then 0; else divs := ifactors(n)[2] ; add( op(1, i), i=divs) ; fi ; end: A134382 := proc(n) option remember ; local k, kmin ; if n = 1 then kmin := 1 ; else kmin := procname(n-1)+1 ; fi ; for k from kmin do if numtheory[sigma](k) = n* numtheory[tau](k)*A008472(k) then RETURN(k) ; fi ; od: end: for n from 1 to 30 do print( A134382(n)) ; od: # R. J. Mathar, Nov 16 2007, Jun 24 2009 MATHEMATICA sopf[1] = 0; sopf[n_] := Total[FactorInteger[n][[All, 1]]]; a[n_] := a[n] = For[k = If[n == 1, 1, a[n-1] + 1], True, k++, If[DivisorSigma[1, k] == n*DivisorSigma[0, k]*sopf[k], Return[k]]]; Table[Print[a[n]]; a[n], {n, 1, 32}] (* Jean-François Alcover, Sep 12 2013 *) PROG lista(nn) = {lasta = 2; for (n=1, nn, k = lasta; while ((f = factor(k)) && (n*numdiv(k)*sum(j=1, #f~, f[j, 1]) != sigma(k)), k++); print1(k, ", "); lasta = k; ); } \\ Michel Marcus, Feb 25 2016 CROSSREFS Cf. A134383, A134384, A134385, A134386. Sequence in context: A264308 A328174 A236988 * A105939 A054389 A253003 Adjacent sequences:  A134379 A134380 A134381 * A134383 A134384 A134385 KEYWORD more,nonn AUTHOR Enoch Haga, Oct 23 2007 EXTENSIONS Edited by R. J. Mathar, Nov 16 2007 A-number in formula and Maple program corrected by R. J. Mathar, Jun 24 2009 a(32) from R. J. Mathar, Feb 05 2010 STATUS approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)