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A325701 Nonprime Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer. 0
1, 9, 25, 49, 77, 121, 125, 169, 221, 245, 289, 323, 343, 361, 375, 437, 529, 841, 899, 961, 1331, 1369, 1517, 1681, 1763, 1849, 1859, 2021, 2197, 2209, 2401, 2773, 2809, 2873, 3127, 3481, 3721, 3757, 4087, 4489, 4757, 4913, 5041, 5183, 5329, 5929, 6137, 6241 (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..48.

EXAMPLE

The sequence of terms together with their prime indices begins:

     1: {}

     9: {2,2}

    25: {3,3}

    49: {4,4}

    77: {4,5}

   121: {5,5}

   125: {3,3,3}

   169: {6,6}

   221: {6,7}

   245: {3,4,4}

   289: {7,7}

   323: {7,8}

   343: {4,4,4}

   361: {8,8}

   375: {2,3,3,3}

   437: {8,9}

   529: {9,9}

   841: {10,10}

   899: {10,11}

   961: {11,11}

For example, the sequence contains 245 because the prime indices of 245 are {3,4,4}, with reciprocal sum 1/6 + 1/24 + 1/24 = 1/4.

MATHEMATICA

Select[Range[1000], !PrimeQ[#]&&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, A316854, A316857, A325618, A325620, A325622, A325623.

Sequence in context: A247687 A075026 A113659 * A113745 A016754 A110487

Adjacent sequences:  A325698 A325699 A325700 * A325702 A325703 A325704

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 17 2019

STATUS

approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)