A265128 Nonprimes excluding numbers of the forms 2*p and p^i where p is a prime and i is a positive integer.

0, 1, 12, 15, 18, 20, 21, 24, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 51, 52, 54, 55, 56, 57, 60, 63, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 84, 85, 87, 88, 90, 91, 92, 93, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114, 115, 116

Offset

1,3

Links

Table of n, a(n) for n=1..62.

Mathematica

Select[Range@ 120, And[! PrimeQ@ #, Nand[EvenQ@ #, PrimeQ[#/2]], ! PrimePowerQ@ #] &] (* Michael De Vlieger, Dec 02 2015 *)

Prog

(PARI) isok(n) = ! (isprime(n) || (! (n%2) && isprime(n/2)) || isprimepower(n)); \\ Michel Marcus, Dec 02 2015
(Python)
from sympy import primepi, integer_nthroot
def A265128(n):
    def f(x): return int(n-1+sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length()))+primepi(x>>1))-(x>=4)
    m, k = n-1, f(n-1)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jun 09 2026

Crossrefs

Cf. A000961, A024619, A100484, A264828.

Sequence in context: A247542 A281880 A153047 * A243021 A164782 A207830

Adjacent sequences: A265125 A265126 A265127 * A265129 A265130 A265131

Keyword

nonn,easy

Author

Giovanni Teofilatto, Dec 02 2015

Status

approved