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A328867 Heinz numbers of integer partitions in which no two distinct parts are relatively prime. 6
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 37, 39, 41, 43, 47, 49, 53, 57, 59, 61, 63, 64, 65, 67, 71, 73, 79, 81, 83, 87, 89, 91, 97, 101, 103, 107, 109, 111, 113, 115, 117, 121, 125, 127, 128, 129, 131, 133, 137, 139, 147, 149 (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).

A partition with no two distinct parts relatively prime is said to be intersecting.

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

The sequence of terms together with their prime indices begins:

    1: {}

    2: {1}

    3: {2}

    4: {1,1}

    5: {3}

    7: {4}

    8: {1,1,1}

    9: {2,2}

   11: {5}

   13: {6}

   16: {1,1,1,1}

   17: {7}

   19: {8}

   21: {2,4}

   23: {9}

   25: {3,3}

   27: {2,2,2}

   29: {10}

   31: {11}

   32: {1,1,1,1,1}

MATHEMATICA

Select[Range[100], And@@(GCD[##]>1&)@@@Subsets[PrimePi/@First/@FactorInteger[#], {2}]&]

CROSSREFS

These are the Heinz numbers of the partitions counted by A328673.

The strict case is A318719.

The relatively prime version is A328868.

A ranking using binary indices is A326910.

The version for non-isomorphic multiset partitions is A319752.

The version for divisibility (instead of relative primality) is A316476.

Cf. A000837, A056239, A112798, A200976, A289509, A303283, A305843, A318715, A318716, A328336.

Sequence in context: A273200 A014567 A324769 * A326536 A322902 A302040

Adjacent sequences:  A328864 A328865 A328866 * A328868 A328869 A328870

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 30 2019

STATUS

approved

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Last modified February 22 12:33 EST 2020. Contains 332136 sequences. (Running on oeis4.)