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A055709 Numbers k such that k | sigma_5(k). 10
1, 6, 22, 28, 66, 120, 198, 264, 308, 366, 440, 604, 672, 924, 984, 1320, 1464, 1694, 1717, 2013, 2296, 2464, 2574, 2970, 3434, 3608, 3960, 4026, 4228, 4598, 4920, 5082, 5151, 5348, 6200, 6600, 6644, 6776, 6868, 6888, 7320, 7392, 8052, 8128, 9504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

sigma_5(k) is the sum of the 5th powers of the divisors of k (A001160).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..7000

Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

MAPLE

with(numtheory);

A055709:=proc(q)

local a, i, n;

for n from 1 to q do

  a:=divisors(n); if frac(add(a[i]^5, i=1..nops(a))/n)=0 then print(n);

fi; od; end:

A055709(100000);  # Paolo P. Lava, Dec 07 2012

MATHEMATICA

Do[If[Mod[DivisorSigma[5, n], n]==0, Print[n]], {n, 1, 15000}]

Select[Range[10000], Divisible[DivisorSigma[5, #], #]&] (* Harvey P. Dale, Aug 09 2013 *)

PROG

(PARI) is(n)=sigma(n, 5)%n==0 \\ Charles R Greathouse IV, Feb 01 2013

CROSSREFS

Cf. A001160.

Cf. A055710, A055711, A055712, A055713.

Sequence in context: A242592 A044448 A111036 * A276795 A037204 A296981

Adjacent sequences:  A055706 A055707 A055708 * A055710 A055711 A055712

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 09 2000

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)