A325623 Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.

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

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