

A046839


Numbers n such that the number of divisors of n divides the sum of cubes of divisors of n.


1



1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102, 103
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OFFSET

1,2


COMMENTS

First 42 terms agree with A003601 but a[ 43 ]=64 is not present in A003601.


LINKS

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


EXAMPLE

a[ 43 ] = 64. The sigma[ k,64 ] values for k=0,1,2,3 are as follows: 7,127,5461 and 299593. While 7 does not divide sum of divisors, 127, it divides the sum of d^3 values: Sum[ d^3 ]=299593=7*127*337


MAPLE

with(numtheory); List046839:=proc(q) local a, b, k, n;
for n from 1 to q do a:=divisors(n); b:=add(a[k]^3, k=1..nops(a));
if type(b/tau(n), integer) then print(n); fi; od; end:
List046839 (10^6); # Paolo P. Lava, Apr 11 2013


MATHEMATICA

Select[Range[103], Divisible[DivisorSigma[3, #], DivisorSigma[0, #]] &] (* Jayanta Basu, Jun 29 2013 *)


PROG

(MAGMA) [n: n in [1..110]  IsZero(DivisorSigma(3, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013


CROSSREFS

Cf. A003601, A020486.
Sequence in context: A092559 A242076 A064728 * A003601 A216782 A072600
Adjacent sequences: A046836 A046837 A046838 * A046840 A046841 A046842


KEYWORD

nonn


AUTHOR

Labos Elemer


STATUS

approved



