A382831 a(n) is the n-th n-almost-prime that is a partial sum of the sequence of n-almost-primes.

2, 10, 964, 1804, 7820, 48120, 830817, 4895208, 11308160, 162802560, 394129476, 3763612800, 19823090472, 1018716103620, 9744542956800, 3989325082624, 329306801920000, 2978224618328064, 11804664377696256, 128906665137012736

Offset: 1

Author

Robert Israel, Apr 28 2025

Keywords

• nonn

Examples

			The first three members of A086062 that are 3-almost-primes are 8 = 2^3, 20 = 2^2 * 5 = 8 + 12, and 964 = 2^2 * 241 = 8 + 12 + 18 + ... + 92, so a(3) = 964.
		

Crossrefs

Cf. A007504, A062198, A086062, A086046, A086047, A086052, A086059, A086061.

Programs

Maple

f:= proc(n) uses priqueue;
  local pq,t,s,x,p,i,count;
  initialize(pq);
  insert([-2^n,2$n],pq);
  s:= 0; count:= 0:
  do
    t:= extract(pq);
    x:= -t[1];
    s:= s + x;
    if numtheory:-bigomega(s) = n  then count:= count+1; if count = n then return s fi fi;
    p:= nextprime(t[-1]);
    for i from n+1 to 2 by -1 while t[i] = t[-1] do
          insert([t[1]*(p/t[-1])^(n+2-i), op(t[2..i-1]), p$(n+2-i)], pq)
    od;
  od
end proc:
map(f, [$1..20]);