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 A221219 Numbers n such that sigma(n) divides sum_{d|n} sigma(d). 6
 1, 198, 608, 4680, 11322, 20826, 56608, 60192, 179424, 1737000, 2578968, 3055150, 3441888, 5604192, 6008184, 6331104, 302459850, 320457888, 477229032, 565344850, 579667086, 589459104, 731925000, 766073448, 907521650, 928765600, 3586977576, 3732082848, 6487717600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A066218 is a subset of this sequence. Numbers n such that A000203(n) divides A007429(n). Jaroslav Krizek, Dec 22 2018 Corresponding values of (Sum_{d|k} sigma(d)) / sigma(k)  for numbers k from this sequence: 1, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, ... - Jaroslav Krizek, Dec 22 2018 LINKS EXAMPLE 4680 is in the sequence because sigma(4680)=16380, its proper divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 26, 30, 36, 39, 40, 45, 52, 60, 65, 72, 78, 90, 104, 117, 120, 130, 156, 180, 195, 234, 260, 312, 360, 390, 468, 520, 585, 780, 936, 1170, 1560, 2340 and the sum of their sigma's is 32760. Finally 32760/16380=2. MAPLE with(numtheory); A221219:=proc(q) local a, b, j, n; for n from 1 to q do a:=divisors(n); b:=add(sigma(a[j]), j=1..nops(a));   if type(b/sigma(n), integer) then print(n); fi; od; end: A221219(10^10); MATHEMATICA f1[p_, e_] := (p*(p^(e + 1) - 1) - (p - 1)*(e + 1))/(p - 1)^2; f2[p_, e_] := (p^(e+1) - 1)/(p - 1); aQ[1] = True; aQ[n_] := Module[{f = FactorInteger[n]}, Divisible[Times @@ f1 @@@ f, Times @@ f2 @@@ f]]; Select[Range[10^5], aQ] (* Amiram Eldar, Dec 23 2018 *) PROG (MAGMA) [k: k in [1..1000000] | &+[SumOfDivisors(d): d in Divisors(k)] mod  SumOfDivisors(k) eq 0] // Jaroslav Krizek, Dec 22 2018 (PARI) isok(n) = (sumdiv(n, d, sigma(d)) % sigma(n) == 0); \\ Michel Marcus, Dec 22 2018 CROSSREFS Cf. A000203, A066218, A224488, A322655, A322656, A319296. Sequence in context: A075293 A083264 A202526 * A238765 A066218 A304614 Adjacent sequences:  A221216 A221217 A221218 * A221220 A221221 A221222 KEYWORD nonn AUTHOR Paolo P. Lava, Feb 22 2013 EXTENSIONS a(10)-a(28) from Donovan Johnson, Apr 05 2013 1 prepended by Jaroslav Krizek, Dec 22 2018 STATUS approved

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Last modified April 24 22:03 EDT 2019. Contains 322446 sequences. (Running on oeis4.)