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Primes p having at least one partition into distinct divisors of p + 1.
8

%I #9 Oct 04 2020 11:55:34

%S 3,5,7,11,17,19,23,29,31,41,47,53,59,71,79,83,89,103,107,127,131,139,

%T 149,167,179,191,197,199,223,227,233,239,251,263,269,271,293,307,311,

%U 347,349,359,367,379,383,389,419,431,439,449,461,463,467,479,499,503

%N Primes p having at least one partition into distinct divisors of p + 1.

%H Amiram Eldar, <a href="/A085498/b085498.txt">Table of n, a(n) for n = 1..2000</a>

%F A085496(a(n)) > 0.

%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[500], PrimeQ[#] && seqQ[#] &] (* _Amiram Eldar_, Jan 13 2020 *)

%t Select[Prime[Range[100]],MemberQ[Total/@Subsets[Divisors[#+1]],#]&] (* _Harvey P. Dale_, Oct 04 2020 *)

%Y Subsequence of A085493.

%Y Cf. A085496, A085497, A085499.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 03 2003