

A325044


Heinz numbers of integer partitions whose sum of parts is greater than or equal to their product.


25



2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 52, 53, 56, 58, 59, 60, 61, 62, 64, 67, 68, 71, 72, 73, 74, 76, 79, 80, 82, 83, 84, 86, 88, 89, 92, 94, 96, 97, 101
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OFFSET

1,1


COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose product of prime indices (A003963) is less than or equal to their sum of prime indices (A056239).
The enumeration of these partitions by sum is given by A096276.


LINKS



FORMULA



EXAMPLE

The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
4: {1,1}
5: {3}
6: {1,2}
7: {4}
8: {1,1,1}
9: {2,2}
10: {1,3}
11: {5}
12: {1,1,2}
13: {6}
14: {1,4}
16: {1,1,1,1}
17: {7}
18: {1,2,2}
19: {8}
20: {1,1,3}
22: {1,5}
23: {9}
24: {1,1,1,2}


MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Times@@primeMS[#]<=Plus@@primeMS[#]&]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



