login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325986 Heinz numbers of complete strict integer partitions. 5
1, 2, 6, 30, 42, 210, 330, 390, 462, 510, 546, 714, 798, 2310, 2730, 3570, 3990, 4290, 4830, 5610, 6006, 6090, 6270, 6510, 6630, 7410, 7590, 7854, 8778, 8970, 9282, 9570, 9690, 10230, 10374, 10626, 11310, 11730, 12090, 12210, 12558, 13398, 13566, 14322, 14430 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Strict partitions are counted by A000009, while complete partitions are counted by A126796.

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

An integer partition of n is complete (A126796, A325781) if every number from 0 to n is the sum of some submultiset of the parts.

The enumeration of these partitions by sum is given by A188431.

LINKS

Table of n, a(n) for n=1..45.

FORMULA

Intersection of A005117 (strict partitions) and A325781 (complete partitions).

EXAMPLE

The sequence of terms together with their prime indices begins:

      1: {}

      2: {1}

      6: {1,2}

     30: {1,2,3}

     42: {1,2,4}

    210: {1,2,3,4}

    330: {1,2,3,5}

    390: {1,2,3,6}

    462: {1,2,4,5}

    510: {1,2,3,7}

    546: {1,2,4,6}

    714: {1,2,4,7}

    798: {1,2,4,8}

   2310: {1,2,3,4,5}

   2730: {1,2,3,4,6}

   3570: {1,2,3,4,7}

   3990: {1,2,3,4,8}

   4290: {1,2,3,5,6}

   4830: {1,2,3,4,9}

   5610: {1,2,3,5,7}

MATHEMATICA

hwt[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>PrimePi[p] k]];

Select[Range[1000], SquareFreeQ[#]&&Union[hwt/@Divisors[#]]==Range[0, hwt[#]]&]

CROSSREFS

Cf. A002033, A056239, A103295, A112798, A126796, A188431, A299702, A304793.

Cf. A325780, A325781, A325782, A325788, A325790, A325988.

Sequence in context: A166062 A100194 A229882 * A298759 A127517 A137825

Adjacent sequences:  A325983 A325984 A325985 * A325987 A325988 A325989

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 30 2019

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 June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)