A113851 Numbers whose prime factors are raised to the sixth power.

64, 729, 15625, 46656, 117649, 1000000, 1771561, 4826809, 7529536, 11390625, 24137569, 47045881, 85766121, 113379904, 148035889, 308915776, 594823321, 729000000, 887503681, 1291467969, 1544804416, 1838265625, 2565726409, 3010936384, 3518743761, 4750104241

Offset

1,1

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Formula

a(n) = A005117(n+1)^6. - Nathaniel Johnston, Jun 21 2011

Sum_{n>=1} 1/a(n) = zeta(6)/zeta(12) - 1 = A269404 - 1. - Amiram Eldar, Oct 13 2020

Maple

for n from 2 to 100 do if(numtheory[issqrfree](n))then printf("%d, ", n^6): fi: od: # Nathaniel Johnston, Jun 21 2011

Mathematica

Select[ Range@37^6, Union[Last /@ FactorInteger@# ] == {6} &] (* Robert G. Wilson v *)
Select[Range[2, 37], SquareFreeQ]^6 (* Amiram Eldar, Oct 13 2020 *)

Prog

(PARI) allpwrfact(n, p) = \All prime factors are raised to the power p { local(x, j, ln, y, flag); for(x=4, n, y=Vec(factor(x)); ln = length(y[1]); flag=0; for(j=1, ln, if(y[2][j]==p, flag++); ); if(flag==ln, print1(x", ")); ) }

Crossrefs

Subset of A001014. Superset of A030516.

Nonunit terms of A329332 column 6 in ascending order.

Cf. A005117, A269404.

Sequence in context: A343286 A240845 A153160 * A046455 A092758 A030516

Adjacent sequences: A113848 A113849 A113850 * A113852 A113853 A113854

Keyword

easy,nonn

Author

Cino Hilliard, Jan 25 2006

Extensions

More terms from Robert G. Wilson v, Jan 26 2006

Status

approved