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A088183 Number of ways to write n as a sum of two coprime semiprimes. 4
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 (list; graph; refs; listen; history; text; internal format)
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 A081212

Adjacent sequences:  A088180 A088181 A088182 * A088184 A088185 A088186

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 22 2003

STATUS

approved

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Last modified August 3 21:19 EDT 2021. Contains 346441 sequences. (Running on oeis4.)