A308874 Composite numbers that are neither squares nor oblongs.

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

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 (non-oblongs).

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