A308874 - OEIS

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

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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 (non-oblongs).