cp's OEIS Frontend

A308874 Composite numbers that are neither squares nor oblongs.

%I A308874 #33 Jul 13 2019 01:47:13
%S A308874 8,10,14,15,18,21,22,24,26,27,28,32,33,34,35,38,39,40,44,45,46,48,50,
%T A308874 51,52,54,55,57,58,60,62,63,65,66,68,69,70,74,75,76,77,78,80,82,84,85,
%U A308874 86,87,88,91,92,93,94,95,96,98,99,102,104,105,106,108,111,112,114
%N A308874 Composite numbers that are neither squares nor oblongs.
%C A308874 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.
%C A308874 Some examples (here tau(n) is the number of divisors of n):
%C A308874 tau(8) = 4 and 8 = 22_3, so: beta'(8) = tau(8)/2 - 1 = 1.
%C A308874 tau(15) = 4 and 15 = 1111_2 = 33_4, so beta'(15) = tau(15)/2 - 1 = 1.
%C A308874 tau(18) = 6 and 18 = 33_5 = 22_8, so beta'(18) = tau(18)/2 - 1 = 2.
%C A308874 tau(54) = 8 and 54 = 66_8 = 33_17 = 22_26, so beta'(54) = tau(54)/2 - 1 = 3.
%o A308874 (PARI) isoblong(n) = my(m=sqrtint(n)); m*(m+1)==n;
%o A308874 isok(n) = !isprime(n) && !issquare(n) && !isoblong(n); \\ _Michel Marcus_, Jul 12 2019
%Y A308874 Cf. A002808 (composites), A000290 (squares), A000037 (nonsquares), A002378 (oblongs), A078358 (non-oblongs).
%Y A308874 Subsequences: A326386, A326387, A326388, A326389.
%K A308874 nonn
%O A308874 1,1
%A A308874 _Bernard Schott_, Jul 12 2019