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A046764 Sum of the 4th powers of the divisors of n is divisible by n. 3
1, 34, 84, 156, 364, 492, 1092, 3444, 5617, 6396, 11234, 22468, 33628, 44772, 67404, 100884, 157276, 190978, 292084, 435708, 437164, 471828, 549687, 569772, 709937, 742612, 763912, 876252, 986076, 1099374, 1118480, 1289484, 1311492, 1419874 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Compare with multiply perfect numbers, A007691. Here Sum[ divisors ] is replaced by Sum[ 4th powers of divisors ].

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..200 from T. D. Noe)

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

FORMULA

Mod[ Sigma [ 4, n ], n ]=0.

EXAMPLE

n=84, Sigma[ 4,84 ] = Sum(d^4) = 53771172 = 640133*84 = 640133*n;

n=5617, Sigma[ 4,5617 ] = 995446331475844 = 5617*17722083332, a multiple of n.

MAPLE

with(numtheory);

A046764:=proc(q)

local a, i, n;

for n from 1 to q do

  a:=divisors(n); if frac(add(a[i]^4, i=1..nops(a))/n)=0 then print(n); fi;

od; end:

A046764(100000);  # Paolo P. Lava, Dec 07 2012

MATHEMATICA

Do[If[Mod[DivisorSigma[4, n], n]==0, Print[n]], {n, 1, 2*10^6}]

Select[Range[1500000], Divisible[DivisorSigma[4, #], #]&] (* Harvey P. Dale, Jun 25 2014 *)

PROG

(PARI) is(n)=sigma(n, 4)%n==0 \\ Charles R Greathouse IV, Feb 04 2013

CROSSREFS

Cf. A001159, A007691.

Sequence in context: A066284 A036199 A092223 * A260276 A278311 A213025

Adjacent sequences:  A046761 A046762 A046763 * A046765 A046766 A046767

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

More terms from Robert G. Wilson v, Jun 09 2000

STATUS

approved

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)