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A302696
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Numbers whose prime indices are pairwise coprime. Nonprime Heinz numbers of integer partitions with pairwise coprime parts.
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72
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1, 2, 4, 6, 8, 10, 12, 14, 15, 16, 20, 22, 24, 26, 28, 30, 32, 33, 34, 35, 38, 40, 44, 46, 48, 51, 52, 55, 56, 58, 60, 62, 64, 66, 68, 69, 70, 74, 76, 77, 80, 82, 85, 86, 88, 92, 93, 94, 95, 96, 102, 104, 106, 110, 112, 116, 118, 119, 120, 122, 123, 124, 128, 132
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OFFSET
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1,2
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. Two or more numbers are coprime if no pair 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).
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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Sequence of integer partitions with pairwise coprime parts begins: (), (1), (11), (21), (111), (31), (211), (41), (32), (1111), (311), (51), (2111), (61), (411), (321).
Missing from this list are: (2), (3), (4), (22), (5), (6), (7), (221), (8), (42), (9), (33), (222).
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MAPLE
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filter:= proc(n) local F;
F:= ifactors(n)[2];
if nops(F)=1 then if F[1][1] = 2 then return true else return false fi fi;
if ormap(t -> t[2]>1 and t[1] <> 2, F) then return false fi;
F:= map(t -> numtheory:-pi(t[1]), F);
ilcm(op(F))=convert(F, `*`)
end proc:
select(filter, [$1..200]); # Robert Israel, Sep 10 2020
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MATHEMATICA
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primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[200], Or[#===1, CoprimeQ@@primeMS[#]]&]
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CROSSREFS
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Cf. A000837, A000961, A001222, A005117, A007359, A051424, A275024, A289508, A289509, A298748, A302568, A302569, A302697, A302698.
Sequence in context: A336735 A304711 A324847 * A195125 A228295 A184592
Adjacent sequences: A302693 A302694 A302695 * A302697 A302698 A302699
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Apr 11 2018
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STATUS
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approved
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