A325701 Nonprime Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.

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

Offset: 1

Author

Gus Wiseman, May 17 2019

Keywords

• nonn

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!.

Examples

			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.
		

Crossrefs

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

Reciprocal factorial sum: A002966, A316854, A316857, A325618, A325620, A325622, A325623.

Programs

Mathematica

Select[Range[1000],!PrimeQ[#]&&IntegerQ[1/Total[Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]!]]]&]