OFFSET
1,2
COMMENTS
Numbers that are prime powers p^m, m >= 0, or products of multiple powers of distinct primes p^m where at least 1 prime power p^m is such that m > 1.
Let N = A000027. Analogous to the following sequences:
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
1 is in the sequence because it is the empty product.
Prime p is in the sequence because it is not a composite squarefree number.
Numbers k that have prime power factors p^m | k where at least one prime power factor is such that m > 1 are in the sequence because they are not squarefree composites. Examples include 8, 9, 12, 20, and 36.
MATHEMATICA
Select[Range[103], Nand[SquareFreeQ[#], CompositeQ[#]] &]
PROG
(PARI) isok(k) = (k==1) || isprimepower(k) || !issquarefree(k); \\ Michel Marcus, Aug 24 2023
(Python)
from math import isqrt
from sympy import mobius, primepi
def A363597(n):
if n==1: return 1
def f(x): return n-1+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))-primepi(x)
m, k = n-1, f(n-1)
while m != k:
m, k = k, f(k)
return m # Chai Wah Wu, Aug 02 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Aug 15 2023
STATUS
approved