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A302568 Odd numbers that are either prime or whose prime indices are pairwise coprime. Heinz numbers of integer partitions with pairwise coprime parts all greater than 1. 5
3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 83, 85, 89, 93, 95, 97, 101, 103, 107, 109, 113, 119, 123, 127, 131, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 165, 167, 173, 177, 179 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset systems.

03: {{1}}

05: {{2}}

07: {{1,1}}

11: {{3}}

13: {{1,2}}

15: {{1},{2}}

17: {{4}}

19: {{1,1,1}}

23: {{2,2}}

29: {{1,3}}

31: {{5}}

33: {{1},{3}}

35: {{2},{1,1}}

37: {{1,1,2}}

41: {{6}}

43: {{1,4}}

47: {{2,3}}

51: {{1},{4}}

53: {{1,1,1,1}}

Sequence of integer partitions begins: (2), (3), (4), (5), (6), (3 2), (7), (8), (9), (10), (11), (5 2), (4 3), (12), (13), (14), (15), (7 2), (16), (5 3), (17), (18), (19), (9 2), (20).

MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[1, 400, 2], Or[PrimeQ[#], CoprimeQ@@primeMS[#]]&]

CROSSREFS

Cf. A000961, A001222, A005117, A007359, A007716, A051424, A056239, A076610, A101268, A275024.

Sequence in context: A187929 A272872 A103796 * A294674 A179458 A062086

Adjacent sequences:  A302565 A302566 A302567 * A302569 A302570 A302571

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 10 2018

STATUS

approved

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Last modified February 23 16:17 EST 2020. Contains 332175 sequences. (Running on oeis4.)