A166103 -id:A166103

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A166102

Odd numbers k such that A166100((k-1)/2)/k is not an integer.

+10
4

3, 27, 75, 243, 363, 675, 867, 1587, 1875, 2187, 2523, 3267, 5043, 6075, 6627, 7803, 8427, 9075, 10443, 14283, 15123, 16875, 19683, 20667, 21675, 22707, 23763, 29403, 30603, 34347, 38307, 39675, 43923, 45387, 46875, 51483, 54675

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Conjecture: a(n) = 3*A166103(n). (Checked for terms a(1)-a(92).)

LINKS

A. Karttunen, Table of n, a(n) for n = 1..92

CROSSREFS

a(n) = A005408(A166101(n)). Cf. A166272.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 13 2009

STATUS

approved

A166104

Natural numbers whose prime factors are all congruent to 3 or 5 mod 6 (i.e., are in the sequence A045410).

+10
3

1, 3, 5, 9, 11, 15, 17, 23, 25, 27, 29, 33, 41, 45, 47, 51, 53, 55, 59, 69, 71, 75, 81, 83, 85, 87, 89, 99, 101, 107, 113, 115, 121, 123, 125, 131, 135, 137, 141, 145, 149, 153, 159, 165, 167, 173, 177, 179, 187, 191, 197, 205, 207, 213, 225, 227, 233, 235, 239

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

1 is included, as it has no prime factors at all, thus no prime factors outside of A045410.

LINKS

A. Karttunen, Table of n, a(n) for n = 1..1001

PROG

(MIT Scheme with macro MATCHING-POS by AK:)

(define A166104 (MATCHING-POS 1 1 (lambda (n) (for-all? (factor n) (lambda (p) (or (= 1 p) (= 3 p) (= 5 (modulo p 6))))))))