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A113851
Numbers whose prime factors are raised to the sixth power.
7
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
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
(Python)
from math import isqrt
from sympy import mobius
def A113851(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**6 # Chai Wah Wu, Feb 25 2025
CROSSREFS
Subset of A001014. Superset of A030516.
Nonunit terms of A329332 column 6 in ascending order.
Sequence in context: A343286 A240845 A153160 * A046455 A092758 A030516
KEYWORD
easy,nonn,changed
AUTHOR
Cino Hilliard, Jan 25 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 26 2006
STATUS
approved