

A325179


Heinz numbers of integer partitions such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1.


7



3, 4, 6, 15, 18, 25, 27, 30, 45, 50, 75, 175, 245, 250, 343, 350, 375, 490, 525, 625, 686, 735, 875, 1029, 1225, 1715, 3773, 4802, 5929, 7203, 7546, 9317, 11319, 11858, 12005, 14641, 16807, 17787, 18634, 18865, 26411, 27951, 29282, 29645, 41503, 43923, 46585
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OFFSET

1,1


COMMENTS

The enumeration of these partitions by sum is given by A325181.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).


LINKS

Table of n, a(n) for n=1..47.
Gus Wiseman, Young diagrams for the first 32 terms.


EXAMPLE

The sequence of terms together with their prime indices begins:
3: {2}
4: {1,1}
6: {1,2}
15: {2,3}
18: {1,2,2}
25: {3,3}
27: {2,2,2}
30: {1,2,3}
45: {2,2,3}
50: {1,3,3}
75: {2,3,3}
175: {3,3,4}
245: {3,4,4}
250: {1,3,3,3}
343: {4,4,4}
350: {1,3,3,4}
375: {2,3,3,3}
490: {1,3,4,4}
525: {2,3,3,4}
625: {3,3,3,3}


MATHEMATICA

durf[n_]:=Length[Select[Range[PrimeOmega[n]], Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]][[#]]>=#&]];
codurf[n_]:=If[n==1, 0, Max[PrimeOmega[n], PrimePi[FactorInteger[n][[1, 1]]]]];
Select[Range[1000], codurf[#]durf[#]==1&]


CROSSREFS

Numbers k such that A263297(k)  A257990(k) = 1.
Positions of 1's in A325178.
Cf. A056239, A093641, A112798, A325180, A325181, A325192, A325196, A325198.
Sequence in context: A063477 A168219 A129827 * A308533 A322956 A122727
Adjacent sequences: A325176 A325177 A325178 * A325180 A325181 A325182


KEYWORD

nonn


AUTHOR

Gus Wiseman, Apr 08 2019


STATUS

approved



