A088185 -id:A088185 - cp's OEIS frontend

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

Reinhard Zumkeller, Sep 22 2003

nonn

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

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

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

Cf. A072931, A001358.

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 *)

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

A088184 Numbers that can be written as sum of two coprime semiprimes.

Original entry on oeis.org

13, 19, 23, 25, 29, 31, 34, 35, 37, 39, 41, 43, 44, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 109, 111, 112, 113, 114

Offset: 1

Reinhard Zumkeller, Sep 22 2003

nonn

A088183(a(n))>0; complement of A088185.

			25 = 2*2+3*7, therefore 25 is a term;
2*2+2*11 is the only partition of n=26 into two semiprimes,
gcd(2*2,2*11)=2>1, therefore 26 is not a term.

Cf. A001358.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI