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A302697 Odd numbers whose prime indices are relatively prime. Heinz numbers of integer partitions with no 1's and with relatively prime parts. 6
15, 33, 35, 45, 51, 55, 69, 75, 77, 85, 93, 95, 99, 105, 119, 123, 135, 141, 143, 145, 153, 155, 161, 165, 175, 177, 187, 195, 201, 205, 207, 209, 215, 217, 219, 221, 225, 231, 245, 249, 253, 255, 265, 275, 279, 285, 287, 291, 295, 297, 309, 315, 323, 327, 329 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A prime index of n is a number m such that prime(m) divides n.

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

Sequence of integer partitions with no 1's and with relatively prime parts begins:

015: (3,2)

033: (5,2)

035: (4,3)

045: (3,2,2)

051: (7,2)

055: (5,3)

069: (9,2)

075: (3,3,2)

077: (5,4)

085: (7,3)

093: (11,2)

095: (8,3)

099: (5,2,2)

105: (4,3,2)

119: (7,4)

123: (13,2)

135: (3,2,2,2)

MATHEMATICA

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

Select[Range[1, 200, 2], GCD@@primeMS[#]===1&]

CROSSREFS

Cf. A000837, A000961, A001222, A005117, A007359, A051424, A076078, A101268, A275024, A285572, A289509, A298748, A302568, A302569, A302696, A302698.

Sequence in context: A331551 A180815 A177204 * A154369 A243592 A089966

Adjacent sequences:  A302694 A302695 A302696 * A302698 A302699 A302700

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 11 2018

STATUS

approved

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Last modified February 20 07:28 EST 2020. Contains 332067 sequences. (Running on oeis4.)