A113852 Numbers whose prime factors are raised to the seventh power.

128, 2187, 78125, 279936, 823543, 10000000, 19487171, 62748517, 105413504, 170859375, 410338673, 893871739, 1801088541, 2494357888, 3404825447, 8031810176, 17249876309, 21870000000, 27512614111, 42618442977, 52523350144, 64339296875, 94931877133, 114415582592

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Oct 13 2020: (Start)

a(n) = A005117(n+1)^7.

Sum_{n>=1} 1/a(n) = zeta(7)/zeta(14) - 1. (End)

Mathematica

Select[Range@34^7, Union[Last /@ FactorInteger@# ] == {7} &] (* Robert G. Wilson v, Jan 26 2006 *)
Select[Range[2, 34], SquareFreeQ]^7 (* 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", ")); ) }
(Python)
from math import isqrt
from sympy import mobius
def A113852(n):
    def f(x): return int(n+1-sum(mobius(k)*(x//k**2) for k in range(2, isqrt(x)+1)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m**7 # Chai Wah Wu, Feb 25 2025

Crossrefs

Proper subset of A001015.

Nonunit terms of A329332 column 7 in ascending order.

Cf. A005117, A013665, A013672.

Sequence in context: A050754 A351605 A343287 * A046456 A092759 A056574

Adjacent sequences: A113849 A113850 A113851 * A113853 A113854 A113855

Keyword

easy,nonn,changed

Author

Cino Hilliard, Jan 25 2006

Extensions

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

Status

approved