OFFSET
1,1
COMMENTS
A number n with prime factorization Product_i p_i^(e_i) is in the sequence iff Product_i ((p_i^{e_i*n+1)-1)/(p_i^(e_i+1)-1)) is an integer. - Robert Israel, Jul 19 2016
Does this sequence consist of the even numbers n such that A000005(n) divides A000005(n^n)? The answer is no according to the b-file since 50176 is missing (((2^(10*50176+1)-1)*(7^(2*50176+1)-1)) mod ((2^11-1)*(7^3-1))) = 372438 and (10*50176+1)*(2*50176+1) mod (11*3) = 0). Note that 50176 is the least number with this property.
LINKS
Robert Israel, Table of n, a(n) for n = 1..500
EXAMPLE
4 is a term because sigma(4^4) = 511 is divisible by sigma(4) = 7.
MAPLE
filter:= proc(n) local F, t, b, r;
F:= ifactors(n)[2];
b:= mul(t[1]^(t[2]+1)-1, t=F);
r:= 1;
for t in F do r:= r * (t[1] &^ (t[2]*n+1)-1) mod b od;
r = 0;
end proc:
select(filter, [seq(i, i=2..10^5, 2)]); # Robert Israel, Jul 19 2016
MATHEMATICA
Select[Range[2, 10^4, 2], Divisible[DivisorSigma[1, #^#], DivisorSigma[1, #]] &] (* Michael De Vlieger, Jul 19 2016 *)
PROG
(PARI) /* Requires a large PARI stack to return even the first few terms */
is(n) = Mod(n, 2)==0 && Mod(sigma(n^n), sigma(n))==0 \\ Felix Fröhlich, Jul 19 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jul 18 2016
EXTENSIONS
a(8)-a(22) from Michel Marcus, Jul 19 2016
More terms from Robert Israel, Jul 19 2016
STATUS
approved