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A308874 Composite numbers that are neither squares nor oblongs. 7

%I #33 Jul 13 2019 01:47:13

%S 8,10,14,15,18,21,22,24,26,27,28,32,33,34,35,38,39,40,44,45,46,48,50,

%T 51,52,54,55,57,58,60,62,63,65,66,68,69,70,74,75,76,77,78,80,82,84,85,

%U 86,87,88,91,92,93,94,95,96,98,99,102,104,105,106,108,111,112,114

%N Composite numbers that are neither squares nor oblongs.

%C 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 Some examples (here tau(n) is the number of divisors of n):

%C tau(8) = 4 and 8 = 22_3, so: beta'(8) = tau(8)/2 - 1 = 1.

%C tau(15) = 4 and 15 = 1111_2 = 33_4, so beta'(15) = tau(15)/2 - 1 = 1.

%C tau(18) = 6 and 18 = 33_5 = 22_8, so beta'(18) = tau(18)/2 - 1 = 2.

%C tau(54) = 8 and 54 = 66_8 = 33_17 = 22_26, so beta'(54) = tau(54)/2 - 1 = 3.

%o (PARI) isoblong(n) = my(m=sqrtint(n)); m*(m+1)==n;

%o isok(n) = !isprime(n) && !issquare(n) && !isoblong(n); \\ _Michel Marcus_, Jul 12 2019

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

%Y Subsequences: A326386, A326387, A326388, A326389.

%K nonn

%O 1,1

%A _Bernard Schott_, Jul 12 2019

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)