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A302301 Number of ways to write n as a sum of two distinct semiprimes. 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 3, 2, 0, 1, 3, 3, 2, 1, 3, 3, 2, 2, 4, 3, 2, 1, 4, 5, 3, 2, 1, 2, 3, 2, 5, 3, 2, 2, 5, 6, 6, 1, 3, 5, 3, 3, 4, 4, 3, 2, 6, 7, 5, 3, 3, 3, 4, 3, 5, 5, 3, 2, 7, 7, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,20

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1000 terms from Harvey P. Dale)

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} [Omega(i) = 2] * [Omega(n-i) = 2], where Omega = A001222 and [] is the Iverson bracket.

EXAMPLE

a(19) = 2; 19 = 15+4 = 10+9.

MAPLE

h:= proc(n) option remember; `if`(n=0, 0,

     `if`(numtheory[bigomega](n)=2, n, h(n-1)))

    end:

b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,

     `if`(i>n, 0, x*b(n-i, h(min(n-i, i-1))))+b(n, h(i-1)))), x, 3)

    end:

a:= n-> coeff(b(n, h(n)), x, 2):

seq(a(n), n=0..120);  # Alois P. Heinz, May 26 2021

MATHEMATICA

Table[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[n - i], 2], {i, Floor[(n - 1)/2]}], {n, 100}]

Table[Count[IntegerPartitions[n, {2}], _?(PrimeOmega[#[[1]]]==PrimeOmega[#[[2]]]==2&&#[[1]]!=#[[2]]&)], {n, 90}] (* Harvey P. Dale, Aug 03 2020 *)

PROG

(PARI) a(n) = sum(i=1, (n-1)\2, (bigomega(i)==2)*(bigomega(n-i)==2)); \\ Michel Marcus, Apr 08 2018

CROSSREFS

Cf. A001222, A001358, A072931.

Sequence in context: A068914 A090824 A264620 * A277264 A259538 A099314

Adjacent sequences:  A302298 A302299 A302300 * A302302 A302303 A302304

KEYWORD

nonn,look,easy

AUTHOR

Wesley Ivan Hurt, Apr 04 2018

STATUS

approved

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Last modified June 18 14:26 EDT 2021. Contains 345113 sequences. (Running on oeis4.)