A385646 a(n) is the number of distinct sums of distinct prime factors of n.

0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 3, 1, 1, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 3, 1, 6, 1, 1, 3, 3, 3, 3, 1, 3, 3, 3, 1, 7, 1, 3, 3, 3, 1, 3, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 6, 1, 3, 3, 1, 3, 7, 1, 3, 3, 6, 1, 3, 1, 3, 3, 3, 3, 7, 1, 3, 1, 3, 1, 7, 3, 3, 3, 3

Offset

1,6

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Formula

a(n) < A385646(n).

Example

The a(18) = 3 distinct sums of distinct prime factors of 18 = 2*3^2 are 2, 3 and 2 + 3.
The a(42) = 7 distinct sums of distinct prime factors of 42 = 2*3*7 are 2, 3, 7, 2 + 3 = 5, 2 + 7 = 9, 3 + 7 = 10, 2 + 3 + 7 = 12.
The a(30) = 6 distinct sums of distinct prime factors of 30 = 2*3*5 are 2, 3, 2 + 3 = 5, 2 + 5 = 7, 3 + 5 = 8, 2 + 3 + 5 = 10.

Maple

A385646:=proc(n)
    local b, k, l, i, j;
    l:=[seq(i[1], i in ifactors(n)[2])]:
    b:=proc(m, i)
        option remember;
        `if`(m=0, 1, `if`(i<1, 0, b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i-1))))
    end;
    return nops(select(x->x>0, [seq(b(k, nops(l)), k=1..add(l))]))
    end:
seq(A385646(n), n=1..85);

Crossrefs

Cf. A000040, A001221, A119347, A385645.

Sequence in context: A243915 A367482 A367095 * A309307 A325446 A337322

Adjacent sequences: A385643 A385644 A385645 * A385647 A385648 A385649

Keyword

nonn,easy

Author

Felix Huber, Jul 11 2025

Status

approved