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A302696 Numbers whose prime indices are pairwise coprime. Nonprime Heinz numbers of integer partitions with pairwise coprime parts. 72
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 (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 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

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

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).

MAPLE

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

MATHEMATICA

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

Select[Range[200], Or[#===1, CoprimeQ@@primeMS[#]]&]

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 11 2018

STATUS

approved

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Last modified February 27 23:23 EST 2021. Contains 341694 sequences. (Running on oeis4.)