%I #9 Jan 13 2020 09:33:15
%S 2,13,37,43,61,67,73,97,101,109,113,137,151,157,163,173,181,193,211,
%T 229,241,257,277,281,283,313,317,331,337,353,373,397,401,409,421,433,
%U 443,457,487,491,523,541,547,563,577,601,613,617,631,641,653,661,673,677
%N Primes p having no partition into distinct divisors of p+1.
%H Amiram Eldar, <a href="/A085497/b085497.txt">Table of n, a(n) for n = 1..4000</a>
%F A085496(a(n)) = 0.
%e 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.
%t 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 *)
%Y Subsequence of A085492.
%Y Cf. A085496, A085498.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jul 03 2003
%E More terms from _Amiram Eldar_, Jan 13 2020