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A360713
Sum of all prime encoded perfect partitions of n.
3
1, 2, 4, 14, 16, 70, 64, 280, 356, 850, 1024, 4630, 4096, 10738, 20820, 47264, 65536, 176712, 262144, 643214, 1129572, 2246994, 4194304, 9716880, 17011472, 34785250, 68859688, 139829626, 268435456, 560518826, 1073741824, 2192136576, 4335013860, 8679894658
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=1..A002033(n)} A258119(n,k).
MAPLE
b:= proc(n, l) option remember; `if`(n=1,
mul(ithprime(mul(l[j], j=1..i-1))^(l[i]-1), i=1..nops(l)),
add(b(n/d, [l[], d]), d=numtheory[divisors](n) minus{1}))
end:
a:= n-> b(n+1, []):
seq(a(n), n=0..33);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 1, Product[Prime[Product[l[[j]], {j, 1, i - 1}]]^(l[[i]] - 1), {i, 1, Length[l]}], Sum[b[n/d, Append[l, d]], {d, Divisors[n]~Complement~{1}}]];
a[n_] := b[n + 1, {}];
Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Nov 21 2023, after Alois P. Heinz *)
CROSSREFS
Row sums of A258119.
Sequence in context: A173338 A054600 A077570 * A253444 A336821 A299488
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 21 2023
STATUS
approved