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, 36, 63, 72, 75, 80, 135, 144, 243, 12, 30, 36, 40, 42, 72, 84, 90, 96, 100, 162, 180, 192, 324, 13, 33, 40, 45, 48, 49, 81, 96, 105, 108, 112, 120, 125, 189, 216, 225, 240, 256, 405, 432, 729

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

Sean A. Irvine, Table of n, a(n) for n = 0..10000

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 triangle begins:
  0 | 1
  1 | (empty)
  2 | 3
  3 | 4
  4 | 5 9
  5 | 6 12
  6 | 7 15 16 27
  7 | 8 18 20 36
  ...

Maple

with(combinat);
A122401_row := proc(n)
    local e, a, L;
    L := [] ;
    for e in sort(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 [Updated for AS order by Sean A. Irvine, Oct 04 2025]

Prog

(PARI)
Row(n)={[prod(k=1, #p, p[k]+1) | p<-partitions(n), #p==0 || p[1]>1]}
{ for(n=0, 10, print(Row(n))) } \\ Andrew Howroyd, Oct 04 2025

Crossrefs

Cf. A122172, A001694, A036035, A079274 (row sums), A122402.

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

Some terms reordered by Andrew Howroyd, Oct 04 2025

Status

approved