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

Author

Alford Arnold, Sep 01 2006

Keywords

• easy
• nonn
• tabf

Comments

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

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

Examples

			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
		

Crossrefs

Cf. A122172 A079274 A122402, A316532.

Programs

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

Extensions

Extended by R. J. Mathar, Aug 28 2018