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!)
A325460 Heinz numbers of integer partitions with strictly increasing differences (with the last part taken to be 0). 9
1, 2, 3, 5, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 67, 69, 71, 73, 74, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 122, 123, 127, 129, 130, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).

The enumeration of these partitions by sum is given by A179269.

LINKS

Table of n, a(n) for n=1..63.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

EXAMPLE

The sequence of terms together with their prime indices begins:

    1: {}

    2: {1}

    3: {2}

    5: {3}

    7: {4}

   10: {1,3}

   11: {5}

   13: {6}

   14: {1,4}

   17: {7}

   19: {8}

   22: {1,5}

   23: {9}

   26: {1,6}

   29: {10}

   31: {11}

   33: {2,5}

   34: {1,7}

   37: {12}

   38: {1,8}

MATHEMATICA

primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];

Select[Range[100], Less@@Differences[Append[primeptn[#], 0]]&]

CROSSREFS

A subsequence of A005117.

Cf. A007294, A056239, A112798, A179269, A325327, A325362, A325364, A325367, A325388, A325390, A325395, A325398, A325456, A325461.

Sequence in context: A118241 A325160 A258613 * A002269 A327445 A325119

Adjacent sequences:  A325457 A325458 A325459 * A325461 A325462 A325463

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 03 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 January 28 10:02 EST 2020. Contains 331319 sequences. (Running on oeis4.)