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A076290 Sum of the semiprime divisors of n. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A semiprime is a product of two primes.

LINKS

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

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

EXAMPLE

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

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}]

PROG

(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

CROSSREFS

Cf. A001222, A001358.

Sequence in context: A210625 A210615 A179312 * A198224 A178105 A178109

Adjacent sequences:  A076287 A076288 A076289 * A076291 A076292 A076293

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Nov 24 2002

STATUS

approved

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Last modified September 27 10:28 EDT 2021. Contains 347689 sequences. (Running on oeis4.)