A325505 - OEIS

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A325505

Heinz number of the set of Heinz numbers of all strict integer partitions of n.

2, 3, 5, 143, 493, 62651, 26718511, 22017033127, 44220524211551, 52289759420183033963, 546407750301194131199484983, 8362548333129019658779663581495109, 1828111016191440393570169991636207115709029581, 1059934964500839879758659437301868941873808925011368355891

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OFFSET

0,1

COMMENTS

The Heinz number of a set or sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Also Heinz numbers of rows of A246867 (squarefree numbers arranged by sum of prime indices A056239).

LINKS

Table of n, a(n) for n=0..13.

Index entries for sequences related to Heinz numbers

FORMULA

a(n) = Product_{i = 1..A000009(n)} prime(A246867(n,i)).

A001221(a(n)) = A001222(a(n)) = A000009(n).

A056239(a(n)) = A147655(n).

A003963(a(n)) = A325506(n).

EXAMPLE

The strict integer partitions of 5 are {(5), (4,1), (3,2)}, with Heinz numbers {11,14,15}, with Heinz number prime(11)*prime(14)*prime(15) = 62651, so a(6) = 62651.

The sequence of terms together with their prime indices begins:

2: {1}

3: {2}

5: {3}

143: {5,6}

493: {7,10}

62651: {11,14,15}

26718511: {13,21,22,30}

22017033127: {17,26,33,35,42}

44220524211551: {19,34,39,55,66,70}

52289759420183033963: {23,38,51,65,77,78,105,110}

546407750301194131199484983: {29,46,57,85,91,102,130,154,165,210}

MATHEMATICA

Table[Times@@Prime/@(Times@@Prime/@#&/@Select[IntegerPartitions[n], UnsameQ@@#&]), {n, 7}]

CROSSREFS

Cf. A001222, A003963, A015723, A056239, A066189, A112798, A145519, A147655, A215366, A246867, A325500 (non-strict version), A325504, A325506, A325512, A325513.

Sequence in context: A041343 A229349 A160600 * A366642 A319609 A140551

Adjacent sequences: A325502 A325503 A325504 * A325506 A325507 A325508

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 07 2019

STATUS

approved