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

Author

Bernard Schott, Jul 12 2019

Keywords

• nonn

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.

Crossrefs

Cf. A002808 (composites), A000290 (squares), A000037 (nonsquares), A002378 (oblongs), A078358 (non-oblongs).

Subsequences: A326386, A326387, A326388, A326389.

Programs

PARI

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