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A046870 Sigma(1,n) divides Sigma(4,n). 2
1, 4, 9, 16, 20, 25, 36, 49, 50, 64, 81, 100, 117, 121, 144, 169, 180, 196, 225, 242, 256, 289, 324, 325, 361, 400, 441, 450, 468, 484, 500, 529, 576, 578, 605, 625, 650, 676, 729, 784, 800, 841, 900, 961, 980, 1024, 1025, 1058, 1089, 1156, 1225, 1280, 1296 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).

sigma_2(n) is the sum of the squares of the divisors of n (A001157).

sigma_4(n) is the sum of the 4th powers of the divisors of n (A001159).

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000

EXAMPLE

n=a(18)=196 of which divisor power sums for k=0,1,2,3,4 are 9,399,51471, 8613489, 1574446419. Sigma_1=399 and Sigma_4=51471*30589=399*129*30589. Thus Both Sigma_2 and Sigma_1 divide Sigma_4.

MAPLE

with(numtheory);

List046870:=proc(q) local a, b, k, n;

for n from 1 to q do

  a:=divisors(n); b:=add(a[k]^4, k=1..nops(a));

  if type(b/sigma(n), integer) then print(n); fi;

od; end: List046870(10^6); # Paolo P. Lava, Apr 10 2013

CROSSREFS

Has large overlap with A020487.

Sequence in context: A010441 A046871 A020487 * A313335 A313336 A313337

Adjacent sequences:  A046867 A046868 A046869 * A046871 A046872 A046873

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)