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A318588 Heinz numbers of integer partitions whose sum of reciprocals squared is an integer. 5
1, 2, 4, 8, 16, 32, 64, 81, 128, 162, 256, 324, 512, 648, 1024, 1296, 2048, 2592, 4096, 5184, 6561, 8192, 8775, 10368, 13122, 16384, 17550, 20736, 26244, 32768, 35100, 41472, 52488, 64827, 65536, 70200, 82944, 104976, 129654, 131072, 140400, 165888, 209952 (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).

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

Sequence of integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (11), (111), (1111), (11111), (111111), (2222), (1111111), (22221), (11111111), (222211), (111111111), (2222111).

MATHEMATICA

Select[Range[10000], IntegerQ[Total[If[#==1, {}, Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]^2]]]]&]

CROSSREFS

Cf. A001222, A056239, A058360, A112798, A289506, A289507, A316855, A316857.

Cf. A318584, A318585, A318586, A318587, A318589.

Sequence in context: A115424 A225878 A272985 * A008881 A208743 A247213

Adjacent sequences:  A318585 A318586 A318587 * A318589 A318590 A318591

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 29 2018

STATUS

approved

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Last modified May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)