login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299200 Number of twice-partitions whose domain is the integer partition with Heinz number n. 10
1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 11, 5, 6, 1, 15, 4, 22, 3, 10, 7, 30, 2, 9, 11, 8, 5, 42, 6, 56, 1, 14, 15, 15, 4, 77, 22, 22, 3, 101, 10, 135, 7, 12, 30, 176, 2, 25, 9, 30, 11, 231, 8, 21, 5, 44, 42, 297, 6, 385, 56, 20, 1, 33, 14, 490, 15, 60, 15, 627, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

LINKS

Table of n, a(n) for n=1..72.

FORMULA

Multiplicative with a(prime(n)) = A000041(n).

EXAMPLE

The a(15) = 6 twice-partitions: (3)(2), (3)(11), (21)(2), (21)(11), (111)(2), (111)(11).

MATHEMATICA

Table[Times@@Cases[FactorInteger[n], {p_, k_}:>PartitionsP[PrimePi[p]]^k], {n, 100}]

PROG

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = numbpart(primepi(f[k, 1])); ); factorback(f); } \\ Michel Marcus, Feb 26 2018

CROSSREFS

Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299201, A299202, A299203.

Sequence in context: A064989 A290099 A250479 * A321272 A321270 A030067

Adjacent sequences:  A299197 A299198 A299199 * A299201 A299202 A299203

KEYWORD

nonn,mult

AUTHOR

Gus Wiseman, Feb 05 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)