A218578 The number of times n occurs in A095972.

2, 1, 3, 1, 1, 3, 2, 0, 2, 2, 2, 1, 2, 1, 3, 1, 2, 0, 4, 0, 2, 2, 1, 2, 0, 2, 2, 1, 3, 1, 2, 1, 2, 3, 0, 1, 2, 2, 1, 1, 2, 1, 2, 0, 3, 1, 2, 1, 2, 0, 4, 1, 2, 3, 2, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 3, 3, 0, 4, 1, 2, 0, 2, 1, 3, 2, 0, 0, 3, 1, 0, 3, 2, 3, 0, 1, 3

Offset: 0

Author

Dmitri Kamenetsky, Nov 03 2012

Keywords

• nonn

Comments

Alternative definition: a(n) = number of k such that A000224(k) = k - n.

Examples

			a(0) is 2, because 0 occurs only twice in A095972. a(1) is 1, because 1 occurs only once in A095972.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000224, A095972, A218620 (greedy inverse).

Programs

Maple

A218578 := proc(n)
    local f;
    f := 0 ;
    for q from 1 to 2*n+2 do
        if A095972(q) = n then
            f := f+1 ;
        end if;
    end do:
    f ;
end proc: # R. J. Mathar, Nov 05 2012

Mathematica

nn = 100; t = Table[Length[Complement[Range[n-1], Union[Mod[Range[n]^2, n]]]], {n, 2*nn + 2}]; Table[Count[t, n], {n, 0, nn}] (* T. D. Noe, Nov 06 2012 *)

Python

from math import prod
from sympy import factorint
def A218578(n): return sum(1 for i in range(1,2*n+3) if n==i-prod((p**(e+1)//((p+1)*(q:=1+(p==2)))>>1)+q for p, e in factorint(i).items())) # Chai Wah Wu, Oct 07 2024