A303282 Numbers whose prime indices have no common divisor other than 1 but are not pairwise coprime.

18, 36, 42, 45, 50, 54, 72, 75, 78, 84, 90, 98, 99, 100, 105, 108, 114, 126, 130, 135, 144, 150, 153, 156, 162, 168, 174, 175, 180, 182, 195, 196, 198, 200, 207, 210, 216, 222, 225, 228, 230, 231, 234, 242, 245, 250, 252, 258, 260, 266, 270, 275, 279, 285, 288

Offset

1,1

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.

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..55.

Example

The sequence of integer partitions whose Heinz numbers belong to this sequence begins (221), (2211), (421), (322), (331), (2221), (22111), (332), (621), (4211), (3221), (441), (522), (3311), (432), (22211).

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[400], !CoprimeQ@@primeMS[#]&&GCD@@primeMS[#]===1&]

Crossrefs

Cf. A000837, A001222, A018783, A051424, A056239, A078374, A168532, A289508, A289509, A296150, A298748, A300486, A302569, A302696, A302796, A303138, A303139, A303140, A303283.

Sequence in context: A285318 A040306 A346137 * A073332 A261991 A375397

Adjacent sequences: A303279 A303280 A303281 * A303283 A303284 A303285

Keyword

nonn

Author

Gus Wiseman, Apr 20 2018

Status

approved