A332220 a(n) is the number of Mersenne exponents (terms of A000043) <= n.

0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11

Offset: 1

Author

Antti Karttunen, Feb 09 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..44497

Crossrefs

A left inverse of A000043, partial sums of A332219.

Programs

Mathematica

Accumulate@ Array[Boole@ PrimeQ[2^# - 1] &, 107] (* Michael De Vlieger, Feb 09 2020 *)
With[{mpe=MersennePrimeExponent[Range[47]]},Accumulate[Table[If[ MemberQ[ mpe,n],1,0],{n,120}]]] (* Harvey P. Dale, Aug 22 2021 *)

PARI

A332219(n) = (isprime(n)&&isprime((2^n)-1));
A332220(n) = if(1==n,0,A332219(n)+A332220(n-1));

Formula

a(1) = 0; and for n > 1, a(n) = A332219(n) + a(n-1).

For all n >= 1, a(A000043(n)) = n.