A278801 G.f.: Sum_{k>0} x^prime(k)/(1-x^k).

0, 0, 1, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 3, 2, 3, 2, 4, 1, 5, 2, 3, 1, 5, 2, 3, 3, 4, 1, 4, 1, 7, 3, 2, 1, 5, 2, 4, 3, 4, 1, 6, 2, 6, 2, 3, 2, 5, 1, 5, 3, 5, 2, 5, 2, 4, 3, 3, 1, 9, 1, 6, 3, 3, 2, 3, 3, 7, 3, 4, 1, 7, 1, 6, 2, 5, 3, 5, 1, 7, 4, 3, 1, 6, 1, 6, 6, 4, 1, 5, 1, 7, 3, 4, 3, 5, 2, 7, 2, 6, 1

Offset: 0

Author

Benedict W. J. Irwin, Nov 28 2016

Keywords

• nonn

Comments

New maxima occur at 2,3,5,11,31,59,211,331,619,1759,2341,3049,4343,12373,15431,18691,31667,66643,67651,...

4343 and 15431 are the only composites in the terms displayed above.

If we define a new maximum as greater than or equal to the previous maximum we get

1,2,3,5,7,11,19,23,31,59,131,163,167,197,211,331,467,521,547,...

This is very dense with primes and contains the previous list as a subset.

Programs

Mathematica

NN=200;MM=PrimePi[NN]+1; Table[Boole[n>2]+Sum[Boole[(n>Prime[k])&&(Mod[n-Prime[k]+k-1,k] == 0)], {k, 2, MM}], {n, 1, NN}]

Formula

G.f.: Sum_{k>0} x^prime(k)/(1-x^k).