

A308874


Composite numbers that are neither squares nor oblongs.


5



8, 10, 14, 15, 18, 21, 22, 24, 26, 27, 28, 32, 33, 34, 35, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 102, 104, 105, 106, 108, 111, 112, 114
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OFFSET

1,1


COMMENTS

A characterization: the terms of this sequence have Brazilian representations with repdigits of length = 2 and the number of these representations is beta'(n) = tau(n)/2  1.
Some examples (here tau(n) is the number of divisors of n):
tau(8) = 4 and 8 = 22_3, so: beta'(8) = tau(8)/2  1 = 1.
tau(15) = 4 and 15 = 1111_2 = 33_4, so beta'(15) = tau(15)/2  1 = 1.
tau(18) = 6 and 18 = 33_5 = 22_8, so beta'(18) = tau(18)/2  1 = 2.
tau(54) = 8 and 54 = 66_8 = 33_17 = 22_26, so beta'(54) = tau(54)/2  1 = 3.


LINKS

Table of n, a(n) for n=1..65.


PROG

(PARI) isoblong(n) = my(m=sqrtint(n)); m*(m+1)==n;
isok(n) = !isprime(n) && !issquare(n) && !isoblong(n); \\ Michel Marcus, Jul 12 2019


CROSSREFS

Cf. A002808 (composites), A000290 (squares), A000037 (nonsquares), A002378 (oblongs), A078358 (nonoblongs).
Subsequences: A326386, A326387, A326388, A326389.
Sequence in context: A309065 A048591 A102615 * A030490 A076639 A100319
Adjacent sequences: A308871 A308872 A308873 * A308875 A308876 A308877


KEYWORD

nonn


AUTHOR

Bernard Schott, Jul 12 2019


STATUS

approved



