A122401 Subsequence of A074139 omitting values derived from partitions with a part of size 1.

1, 3, 4, 5, 9, 6, 12, 7, 15, 16, 27, 8, 18, 20, 36, 9, 21, 24, 25, 45, 48, 81, 10, 24, 28, 30, 54, 60, 64, 108, 11, 27, 32, 35, 63, 36, 72, 75, 80, 135, 144, 243, 12, 30, 36, 40, 72, 42, 84, 90, 96, 162, 100, 180, 192, 324, 13, 33, 40, 45, 81, 48, 96, 49, 105, 112, 189, 108, 120, 216, 125, 225, 240, 405, 256, 432, 729, 14, 36, 44, 50, 90, 54

Offset

0,2

Comments

When viewed as a table, row sums are given by sequence A079274.

Corresponds to members of A036035 which are also powerful numbers (A001694).

Links

Table of n, a(n) for n=0..82.

Example

The two cyclic partitions of five are 5 and 3+2 yielding (5+1)=6 and (3+1)*(2+1) = 4*3 = 12
The array begins
1
(empty)
3
4
5 9
6 12
7 15 16 27
8 18 20 36

Maple

A122401_row := proc(n)
    local e, a, L;
    L := [] ;
    for e in ListTools[Reverse](partition(n)) do
        if member(1, e) then
            ;
        else
            a := 1;
            for p in e do
                a := a*(p+1) ;
            end do:
            L := [op(L), a] ;
        end if;
    end do:
    L ;
end proc:
seq(A122401_row(i), i=0..15); # R. J. Mathar, Aug 28 2018

Crossrefs

Cf. A122172 A079274 A122402, A316532.

Sequence in context: A330577 A020863 A215496 * A122403 A349659 A302653

Adjacent sequences: A122398 A122399 A122400 * A122402 A122403 A122404

Keyword

easy,nonn,tabf

Author

Alford Arnold, Sep 01 2006

Extensions

Extended by R. J. Mathar, Aug 28 2018

Status

approved