A365494 a(n) is the smallest number which can be represented as the sum of n distinct n-almost primes in exactly n ways, or -1 if no such number exists.

2, 19, 65, 190, 440, 1160, 2896, 7072, 16832, 40064, 90752, 208640, 476160, 1082880, 2398208, 5310464, 11694080, 25616384, 56475648, 122388480, 266010624, 575012864, 1245446144, 2699034624, 5779750912, 12296650752, 26377977856, 55855546368, 118656860160, 255458279424, 531669975040

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Almost Prime.

Example

For n = 2: 19 = 2*2 + 3*5 = 3*3 + 2*5.

Maple

f:= proc(n) uses priqueue; local pq, S, t, x, y, k, i, p, v, R;
     initialize(pq);
     insert([-2^n, 2$n], pq);
     S[0]:= 1:
     for i from 1 to n do S[i]:= 0 od:
     do
       t:= extract(pq);
       x:= -t[1];
       for i from n to 1 by -1 do
         S[i]:= expand(S[i] + S[i-1] * y^x);
       od;
       if type(S[n], `+`) then
         R:= select(t -> degree(t, y) < x and eval(t, y=1) = n, convert(S[n], list));
         if R <> [] then return min(map(t -> degree(t, y), R)) fi;
       fi;
       p:= nextprime(t[-1]);
       for i from n+1 to 2 by -1 while t[i] = t[-1] do
        v:= x*(p/t[-1])^(n+2-i);
        insert([-v, op(t[2..i-1]), p$(n+2-i)], pq)
       od;
     od;
end proc:
map(f, [$1..19]); # Robert Israel, Jun 10 2025

Crossrefs

Cf. A091538, A365493.

Sequence in context: A204219 A042149 A218547 * A232537 A309341 A079773

Adjacent sequences: A365491 A365492 A365493 * A365495 A365496 A365497

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 07 2023

Extensions

a(5)-a(19) from Robert Israel, Jun 10 2025

More terms from David A. Corneth, Jun 10 2025

Status

approved