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

0,1

Comments

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

Links

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

Example

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

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 *)

Prog

(Python)
from math import prod
from factorint 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

Crossrefs

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

Sequence in context: A212623 A229214 A349685 * A006346 A244740 A088742

Adjacent sequences: A218575 A218576 A218577 * A218579 A218580 A218581

Keyword

nonn

Author

Dmitri Kamenetsky, Nov 03 2012

Status

approved