

A046840


Number of divisors divides sum of 4th powers of divisors.


1



1, 3, 4, 5, 7, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 25, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 100, 101, 103, 105, 107, 108, 109, 111
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Below 1000 the {16,80,81,176,304,324,400,405,464,496,656,784,880,891,944,976} are those numbers which enclosed here but not in A020486, which otherwise is very similar to this sequence.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


EXAMPLE

x=16 with 5 divisors, sigma(k,16) = 5,31,341,46801,69905 for k=0,1,2,3,4 resp. It is seen that sigma(4,16) = 13981*sigma(0,64) = 41*sigma(2,64)*sigma(0,64).


MAPLE

with(numtheory); List046840:=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/tau(n), integer) then print(n); fi; od; end:
List046840 (10^6); # Paolo P. Lava, Apr 11 2013


PROG

(MAGMA) [n: n in [1..120]  IsZero(DivisorSigma(4, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013


CROSSREFS

Cf. A020486, A003601.
Sequence in context: A003312 A022440 A088130 * A057773 A020486 A091428
Adjacent sequences: A046837 A046838 A046839 * A046841 A046842 A046843


KEYWORD

nonn


AUTHOR

Labos Elemer


STATUS

approved



