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

1,6

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

Links

Table of n, a(n) for n=1..49.

Example

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

Prog

(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

Crossrefs

Cf. A116979, A117825.

Sequence in context: A026493 A177431 A145735 * A361081 A213206 A299496

Adjacent sequences: A228940 A228941 A228942 * A228944 A228945 A228946

Keyword

nonn

Author

Jaycob Coleman, Sep 08 2013

Extensions

More terms from Michel Marcus, Sep 10 2013

Status

approved