A378764 Sum of the semiprimes which are less than or equal to n minus the sum of the primes which are less than or equal to n.

0, -2, -5, -1, -6, 0, -7, -7, 2, 12, 1, 1, -12, 2, 17, 17, 0, 0, -19, -19, 2, 24, 1, 1, 26, 52, 52, 52, 23, 23, -8, -8, 25, 59, 94, 94, 57, 95, 134, 134, 93, 93, 50, 50, 50, 96, 49, 49, 98, 98, 149, 149, 96, 96, 151, 151, 208, 266, 207, 207, 146, 208, 208, 208, 273, 273, 206, 206, 275, 275

Offset: 1

Author

Robert G. Wilson v and Luca Bencini-Tibo, Dec 20 2024

Keywords

• sign

Comments

After a(32), a(n) always exceeds 0. See A243906(32).

Examples

			a(6) = 0, because (4+6) - (2+3+5) = 0.
		

Crossrefs

Cf. A001358, A062198, A000040, A007504, A243906.

Programs

Mathematica

a[n_] := Plus @@ Select[ Range@ n, PrimeOmega@ # == 2 &] - Plus @@ Select[ Range@ n, PrimeOmega@ # == 1 &]; Array[a, 70]

PARI

a(n) = my(vf=apply(factor, [1..n])); vecsum(Vec(select(x->(bigomega(x)==2), vf, 1))) - vecsum(Vec(select(x->(bigomega(x)==1), vf, 1))); \\ Michel Marcus, Dec 28 2024