

A325164


Heinz numbers of integer partitions with Durfee square of length 2.


13



9, 15, 18, 21, 25, 27, 30, 33, 35, 36, 39, 42, 45, 49, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 98, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 126, 129, 130, 132, 133, 135, 138, 140
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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).
Also positions of 2 in A257990.
First differs from A105441 in lacking 125.
The Durfee length 1 case is A093641. The enumeration of Durfee length 2 partitions by sum is given by A006918, while that of Durfee length 3 partitions is given by A117485.


LINKS

Table of n, a(n) for n=1..60.
Gus Wiseman, Young diagrams corresponding to the first 36 terms.


EXAMPLE

The sequence of terms together with their prime indices begins:
9: {2,2}
15: {2,3}
18: {1,2,2}
21: {2,4}
25: {3,3}
27: {2,2,2}
30: {1,2,3}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
39: {2,6}
42: {1,2,4}
45: {2,2,3}
49: {4,4}
50: {1,3,3}
51: {2,7}
54: {1,2,2,2}
55: {3,5}
57: {2,8}
60: {1,1,2,3}


MATHEMATICA

durf[n_]:=Length[Select[Range[PrimeOmega[n]], Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]][[#]]>=#&]];
Select[Range[100], durf[#]==2&]


CROSSREFS

Cf. A006918, A056239, A093641, A112798, A115994, A117485, A252464, A257990, A325163, A325170.
Sequence in context: A316752 A110473 A105441 * A093642 A177733 A207675
Adjacent sequences: A325161 A325162 A325163 * A325165 A325166 A325167


KEYWORD

nonn


AUTHOR

Gus Wiseman, Apr 05 2019


STATUS

approved



