%I #48 May 26 2023 20:12:20

%S 1,-1,2,3,-1,6,-1,10,15,14,30,11,42,22,70,105,66,210,110,165,154,330,

%T 182,462,170,770,1155,910,2310,858,2730,1430,2145,2002,4290,1870,6006,

%U 2618,10010,15015,7854,30030,13090,19635,15470,39270,17290,46410,24310,51870

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

%e 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 13 = 2 + 11; products are 13 = 13 and 2*11 = 22; 22 > 13, so a(13) = 22.

%o (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 Cf. A000586, A000792 (the same without condition distinct), A064502 (with min).

%K sign

%O 0,3

%A _Zhao Hui Du_, May 23 2023