A076290 Sum of the semiprime divisors of n.

0, 0, 0, 4, 0, 6, 0, 4, 9, 10, 0, 10, 0, 14, 15, 4, 0, 15, 0, 14, 21, 22, 0, 10, 25, 26, 9, 18, 0, 31, 0, 4, 33, 34, 35, 19, 0, 38, 39, 14, 0, 41, 0, 26, 24, 46, 0, 10, 49, 35, 51, 30, 0, 15, 55, 18, 57, 58, 0, 35, 0, 62, 30, 4, 65, 61, 0, 38, 69, 59, 0, 19, 0, 74, 40, 42, 77, 71, 0

Offset: 1

Author

Joseph L. Pe, Nov 24 2002

Keywords

• easy
• nonn

Comments

A semiprime is a product of two primes.

Inverse Möbius transform of n * c(n), where c = A064911. - Wesley Ivan Hurt, Jul 22 2025

Examples

			The divisors of 12 are 1, 2, 3, 4, 6, 12, of which 4 and 6 are semiprime. Hence a(12) = 4 + 6 = 10.
		

Links

• Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222 (Omega), A001358, A064911.

Programs

Maple

a:= proc(n) local l, m; l:=ifactors(n)[2]; m:=nops(l);
      add(`if`(l[i][2]>1, l[i][1]^2, 0)+
      add(l[i][1]*l[j][1], j=i+1..m), i=1..m)
    end:
seq(a(n), n=1..120);  # Alois P. Heinz, Jul 18 2013

Mathematica

isSP[n_] := Module[{f, l}, f = FactorInteger[n]; l = Length[f]; (l == 2 && f[[1]][[2]] == 1 && f[[2]][[2]] == 1) || (l == 1 && f[[1]][[2]] == 2)]; f[n_] := Module[{a, d, l}, a = {}; d = Divisors[n]; l = Length[d]; For[i = 1, i <= l, i++, If[isSP[d[[i]]], a = Append[a, d[[i]]]]]; a]; Table[Apply[Plus, f[i]], {i, 1, 100}]
ssd[n_]:=Total[Select[Divisors[n],PrimeOmega[#]==2&]]; Array[ssd,80] (* Harvey P. Dale, Jul 29 2025 *)

PARI

a(n) = local(fn, r, om); fn=factor(n); r=om=0; for(i=1,matsize(fn)[1], om+=fn[i,1]; r+=fn[i,1]^2*if(fn[i,2]==1,-1,1)); (r+om^2)\2 \\ Franklin T. Adams-Watters, Jul 26 2009

Formula

a(n) = Sum_{d|n} d * [Omega(d) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jan 28 2021