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A325621 Heinz numbers of integer partitions whose reciprocal factorial sum is an integer. 5
1, 2, 4, 8, 9, 16, 18, 32, 36, 64, 72, 81, 128, 144, 162, 256, 288, 324, 375, 512, 576, 648, 729, 750, 1024, 1152, 1296, 1458, 1500, 2048, 2304, 2592, 2916, 3000, 3375, 4096, 4608, 5184, 5832, 6000, 6561, 6750, 8192, 9216, 10368, 11664, 12000, 13122, 13500 (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..49.

EXAMPLE

The sequence of terms together with their prime indices begins:

      1: {}

      2: {1}

      4: {1,1}

      8: {1,1,1}

      9: {2,2}

     16: {1,1,1,1}

     18: {1,2,2}

     32: {1,1,1,1,1}

     36: {1,1,2,2}

     64: {1,1,1,1,1,1}

     72: {1,1,1,2,2}

     81: {2,2,2,2}

    128: {1,1,1,1,1,1,1}

    144: {1,1,1,1,2,2}

    162: {1,2,2,2,2}

    256: {1,1,1,1,1,1,1,1}

    288: {1,1,1,1,1,2,2}

    324: {1,1,2,2,2,2}

    375: {2,3,3,3}

    512: {1,1,1,1,1,1,1,1,1}

MATHEMATICA

Select[Range[1000], IntegerQ[Total[Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]!]]]&]

CROSSREFS

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

Reciprocal factorial sum: A002966, A058360, A316856, A325619, A325620, A325623.

Sequence in context: A152111 A316856 A324524 * A025611 A049439 A251642

Adjacent sequences:  A325618 A325619 A325620 * A325622 A325623 A325624

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2019

STATUS

approved

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Last modified August 13 18:00 EDT 2022. Contains 356107 sequences. (Running on oeis4.)