A289182 Positions of odd semiprimes in A001358.

3, 6, 7, 9, 11, 13, 15, 17, 18, 19, 20, 23, 24, 26, 28, 30, 31, 32, 34, 36, 37, 39, 40, 42, 43, 44, 46, 48, 49, 51, 53, 54, 56, 57, 59, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 79, 80, 81, 83, 85, 86, 89, 90, 91, 92, 94, 95, 97, 98

Offset: 1

Author

Zak Seidov, Jun 27 2017

Keywords

• nonn

Comments

Complement to A115392.

Crossrefs

Cf. A001358, A115392.

Programs

Mathematica

sp=Select[Range[4,1000],2==PrimeOmega[#]&];Flatten[Position[Mod[sp, 2],1]]

PARI

lista(nn) = vsp = select(x->(bigomega(x)==2), vector(nn, k, k)); select(x->(x%2), vsp, 1); \\ Michel Marcus, Jul 02 2017

Python

from math import isqrt
from sympy import primepi, primerange
def A289182(n):
    def iterfun(f,n=0):
        m, k = n, f(n)
        while m != k: m, k = k, f(k)
        return m
    def f(x): return int(-((t:=primepi(s:=isqrt(x)))*(t-1)>>1)+sum(primepi(x//p) for p in primerange(3,s+1)))
    return f(m:=iterfun(lambda x:int(n+x-f(x)),n))+primepi(m>>1) # Chai Wah Wu, Apr 03 2025

Formula

a(n) ~ n. - Charles R Greathouse IV, Jul 02 2017