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A363266 Maximum product of distinct primes with sum n, or -1 if n is not the sum of distinct primes.

%I A363266 #48 May 26 2023 20:12:20
%S A363266 1,-1,2,3,-1,6,-1,10,15,14,30,11,42,22,70,105,66,210,110,165,154,330,
%T A363266 182,462,170,770,1155,910,2310,858,2730,1430,2145,2002,4290,1870,6006,
%U A363266 2618,10010,15015,7854,30030,13090,19635,15470,39270,17290,46410,24310,51870
%N A363266 Maximum product of distinct primes with sum n, or -1 if n is not the sum of distinct primes.
%e A363266 Expressed as a sum of distinct primes, 12 = 5 + 7 = 2 + 3 + 7. Products are 5*7 = 35 and 2*3*7 = 42; 42 > 35, so a(12) = 42.
%e A363266 13 = 2 + 11; products are 13 = 13 and 2*11 = 22; 22 > 13, so a(13) = 22.
%o A363266 (PARI) alist(n)={local(v); v=vector(n, x, -1); forprime(p=2, n, forstep(h=n, p+1, -1, v[h]=max(v[h], v[h-p]*p)); v[p]=max(v[p], p)); v}
%Y A363266 Cf. A000586, A000792 (the same without condition distinct), A064502 (with min).
%K A363266 sign
%O A363266 0,3
%A A363266 _Zhao Hui Du_, May 23 2023