A085497 Primes p having no partition into distinct divisors of p+1.

2, 13, 37, 43, 61, 67, 73, 97, 101, 109, 113, 137, 151, 157, 163, 173, 181, 193, 211, 229, 241, 257, 277, 281, 283, 313, 317, 331, 337, 353, 373, 397, 401, 409, 421, 433, 443, 457, 487, 491, 523, 541, 547, 563, 577, 601, 613, 617, 631, 641, 653, 661, 673, 677

Offset: 1

Author

Reinhard Zumkeller, Jul 03 2003

Keywords

• nonn

Examples

			p=13, divisors of p+1=13+1=14 that are not greater 13: {1,2,7} with sums of distinct summands 1,2,3=2+1,7,8=7+1,9=7+2 and 10=7+2+1, therefore 13 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4000

Crossrefs

Subsequence of A085492.

Cf. A085496, A085498.

Programs

Mathematica

seqQ[p_] := Module[{d = Most[Divisors[p+1]]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, p}], p] == 0]; Select[Range[700], PrimeQ[#] && seqQ[#] &] (* Amiram Eldar, Jan 13 2020 *)

Formula

A085496(a(n)) = 0.

Extensions

More terms from Amiram Eldar, Jan 13 2020