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!)
A325623 Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer. 6
1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229 (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 reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

The sequence of terms together with their prime indices begins:

    1: {}

    2: {1}

    3: {2}

    5: {3}

    7: {4}

    9: {2,2}

   11: {5}

   13: {6}

   17: {7}

   19: {8}

   23: {9}

   25: {3,3}

   29: {10}

   31: {11}

   37: {12}

   41: {13}

   43: {14}

   47: {15}

   49: {4,4}

   53: {16}

MATHEMATICA

Select[Range[100], IntegerQ[1/Total[Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]!]]]&]

CROSSREFS

Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.

Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316857, A325619, A325621, A325622.

Sequence in context: A090332 A325395 A070566 * A136327 A095415 A326149

Adjacent sequences:  A325620 A325621 A325622 * A325624 A325625 A325626

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 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 May 28 12:02 EDT 2020. Contains 334681 sequences. (Running on oeis4.)