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).
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
Offset: 1
Links
- Carlos Rivera, Puzzle 419. Four SOPF questions, Prime Puzzles.
Crossrefs
Programs
-
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 *) -
PARI
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
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
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
full,fini keywords added by Max Alekseyev, Sep 18 2024
Comments