A088183 Number of ways to write n as a sum of two coprime semiprimes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 4, 1, 0, 1, 4, 0, 2, 0, 1, 0, 3, 0, 4, 0, 1, 2, 5, 0, 6, 0, 1, 3, 1, 0, 4, 1, 3, 0, 6, 0, 5, 3, 1, 2, 3, 0, 5, 0, 3, 2, 7, 0, 1, 3, 4, 1, 4, 0, 6, 2, 2, 3, 6, 0, 7, 1, 4, 2, 6, 1

Offset

1,19

Comments

a(A088184(n))>0, a(A088185(n))=0.

Is a(n)>0 for n>210? see conjecture in A072931.

The graph of this sequence is compelling evidence that 210 is the last term of sequence A088185. - T. D. Noe, Apr 10 2007

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Eric Weisstein's World of Mathematics, Semiprime

Eric Weisstein's World of Mathematics, Relatively Prime

Example

a(64)=3: 64 = 3*3+5*11 = 3*5+7*7 = 5*5+3*13, (A072931(64)=5).

Mathematica

cpspQ[{a_, b_}]:=PrimeOmega[a]==PrimeOmega[b]==2&&CoprimeQ[a, b]; Table[ Count[ IntegerPartitions[n, {2}], _?(cpspQ[#]&)], {n, 110}] (* Harvey P. Dale, Sep 10 2019 *)

Prog

(PARI) a(n)=sum(i=1, n, sum(j=1, i, if (gcd(i, j)==1, if (abs(bigomega(i)-2) +abs(bigomega(j)-2) +abs(n-i-j), 0, 1)))) \\ after A072966; Michel Marcus, Sep 08 2015

Crossrefs

Cf. A072931, A001358.

Sequence in context: A302110 A085983 A285701 * A308470 A070140 A361561

Adjacent sequences: A088180 A088181 A088182 * A088184 A088185 A088186

Keyword

nonn

Author

Reinhard Zumkeller, Sep 22 2003

Status

approved