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A302798 Squarefree numbers that are prime or whose prime indices are pairwise coprime. Heinz numbers of strict integer partitions that either consist of a single part or have pairwise coprime parts. 7
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 41, 43, 46, 47, 51, 53, 55, 58, 59, 61, 62, 66, 67, 69, 70, 71, 73, 74, 77, 79, 82, 83, 85, 86, 89, 93, 94, 95, 97, 101, 102, 103, 106, 107, 109, 110, 113, 118, 119, 122 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A prime index of n is a number m such that prime(m) divides n. Two or more numbers are coprime if no pair of them has a common divisor other than 1. A single number is not considered coprime unless it is equal to 1.

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..64.

EXAMPLE

Sequence of terms together with their sets of prime indices begins:

01 : {}

02 : {1}

03 : {2}

05 : {3}

06 : {1,2}

07 : {4}

10 : {1,3}

11 : {5}

13 : {6}

14 : {1,4}

15 : {2,3}

17 : {7}

19 : {8}

22 : {1,5}

23 : {9}

26 : {1,6}

29 : {10}

30 : {1,2,3}

MATHEMATICA

Select[Range[100], Or[#===1, SquareFreeQ[#]&&(PrimeQ[#]||CoprimeQ@@PrimePi/@FactorInteger[#][[All, 1]])]&]

CROSSREFS

Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A294472, A302242, A302505, A302696, A302697, A302698, A302796, A302797.

Sequence in context: A167171 A087008 A326537 * A294472 A077337 A093501

Adjacent sequences:  A302795 A302796 A302797 * A302799 A302800 A302801

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 13 2018

STATUS

approved

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Last modified May 19 23:13 EDT 2022. Contains 353847 sequences. (Running on oeis4.)