A228943 Number of decompositions of highly composite numbers (A002182) into unordered sums of two primes.

0, 0, 1, 1, 1, 3, 4, 5, 6, 12, 14, 18, 22, 39, 51, 68, 83, 112, 184, 251, 315, 431, 527, 652, 768, 1011, 1128, 1305, 1836, 2344, 3240, 4082, 4955, 5725, 8023, 8723, 10260, 11945, 16771, 21466, 30280, 38583, 46645, 54789, 77430, 85067, 99199, 120742, 154753

Offset: 1

Author

Jaycob Coleman, Sep 08 2013

Keywords

• nonn

Comments

a(n) = A045917(A002182(n)/2) for n>1.

Conjecture: (a) This sequence is strictly increasing beginning with n=5. (b) For all n>2, if p is the greatest prime with p<A002182(n)-1, then A002182(n)-p is prime. This is a strengthening of a conjecture regarding A117825. - Jaycob Coleman, Sep 08 2013

Examples

			a(6)=3, since 24=5+19=7+17=11+13.
		

Crossrefs

Cf. A116979, A117825.

Programs

PARI

nbd(n) = my(s); forprime(p=2, n\2, s+=isprime(n-p)); s;
lista(nn) = {last = 1; print1(nbd(last), ", "); forstep(n=2, nn, 2, if(numdiv(n)> last, last=numdiv(n); print1(nbd(n), ", ")););} \\ Michel Marcus, Sep 10 2013

Extensions

More terms from Michel Marcus, Sep 10 2013