A319299 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A319299

Irregular triangle where T(n,k) is the number of integer partitions of n with GCD equal to the k-th divisor of n.

1, 1, 1, 2, 1, 3, 1, 1, 6, 1, 7, 2, 1, 1, 14, 1, 17, 3, 1, 1, 27, 2, 1, 34, 6, 1, 1, 55, 1, 63, 7, 3, 2, 1, 1, 100, 1, 119, 14, 1, 1, 167, 6, 2, 1, 209, 17, 3, 1, 1, 296, 1, 347, 27, 7, 2, 1, 1, 489, 1, 582, 34, 6, 3, 1, 1, 775, 14, 2, 1, 945, 55, 1, 1, 1254

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Robert Israel, Table of n, a(n) for n = 1..10006 (rows 1 to 1358, flattened)

FORMULA

T(n,k) = A000837(n/A027750(n,k)).

EXAMPLE

Triangle begins:

1 1

2 1

3 1 1

6 1

7 2 1 1

14 1

17 3 1 1

27 2 1

34 6 1 1

55 1

63 7 3 2 1 1

100 1

119 14 1 1

167 6 2 1

209 17 3 1 1

296 1

347 27 7 2 1 1

489 1

582 34 6 3 1 1

MAPLE

# with table A000837 obtained from that sequence

f:= proc(n) local D, d;

D:= sort(convert(numtheory:-divisors(n), list), `>`);

seq(A000837[d], d=D)

end proc:

map(f, [$1..60]); # Robert Israel, Jul 09 2020

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], GCD@@#==k&]], {n, 20}, {k, Divisors[n]}]

CROSSREFS

A regular version is A168532. Row lengths are A000005. Row sums are A000041. First column is A000837.

Cf. A018783, A027750, A078374, A078392, A289508, A289509, A303139, A305563, A319300.

Sequence in context: A191861 A350200 A129761 * A207031 A156248 A324817

Adjacent sequences: A319296 A319297 A319298 * A319300 A319301 A319302

KEYWORD

nonn,tabf,look

AUTHOR

Gus Wiseman, Sep 16 2018

STATUS

approved