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!)
A325235 Heinz numbers of integer partitions with Dyson rank 1 or -1. 3
3, 4, 10, 12, 15, 18, 25, 27, 28, 40, 42, 60, 63, 70, 88, 90, 98, 100, 105, 112, 132, 135, 147, 150, 168, 175, 198, 208, 220, 225, 245, 250, 252, 280, 297, 308, 312, 330, 343, 352, 375, 378, 392, 420, 462, 468, 484, 495, 520, 528, 544, 550, 567, 588, 625, 630 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers whose maximum prime index and number of prime indices counted with multiplicity differ by 1.

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..56.

FindStat, St000145: The Dyson rank of a partition

EXAMPLE

The sequence of terms together with their prime indices begins:

    3: {2}

    4: {1,1}

   10: {1,3}

   12: {1,1,2}

   15: {2,3}

   18: {1,2,2}

   25: {3,3}

   27: {2,2,2}

   28: {1,1,4}

   40: {1,1,1,3}

   42: {1,2,4}

   60: {1,1,2,3}

   63: {2,2,4}

   70: {1,3,4}

   88: {1,1,1,5}

   90: {1,2,2,3}

   98: {1,4,4}

  100: {1,1,3,3}

  105: {2,3,4}

  112: {1,1,1,1,4}

MATHEMATICA

Select[Range[1000], Abs[PrimePi[FactorInteger[#][[-1, 1]]]-PrimeOmega[#]]==1&]

CROSSREFS

Positions of 1's and -1's in A257541.

Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325233, A325234.

Sequence in context: A243681 A242881 A287448 * A135116 A259559 A050187

Adjacent sequences:  A325232 A325233 A325234 * A325236 A325237 A325238

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 13 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 July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)