cp's OEIS Frontend

A326387 Non-oblong composites m such that beta(m) = tau(m)/2 where beta(m) is the number of Brazilian representations of m and tau(m) is the number of divisors of m.

%I A326387 #20 Feb 02 2025 02:25:32
%S A326387 15,21,26,40,57,62,80,85,86,91,93,111,114,124,129,133,146,170,171,172,
%T A326387 183,215,219,222,228,242,259,266,285,292,312,314,333,341,343,365,366,
%U A326387 381,399,422,438,444,455,468,471,482,507,518,532,549,553
%N A326387 Non-oblong composites m such that beta(m) = tau(m)/2 where beta(m) is the number of Brazilian representations of m and tau(m) is the number of divisors of m.
%C A326387 As tau(m) = 2 * beta(m), the terms of this sequence are not squares.
%C A326387 The number of Brazilian representations of a non-oblong number m with repdigits of length = 2 is beta'(n) = tau(n)/2 - 1.
%C A326387 This sequence is the first subsequence of A326380: non-oblong composites which have only one Brazilian representation with three digits or more.
%H A326387 Amiram Eldar, <a href="/A326387/b326387.txt">Table of n, a(n) for n = 1..10000</a>
%H A326387 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Br#Brazilian_numbers">Index entries for sequences related to Brazilian numbers</a>.
%e A326387 tau(m) = 4 and beta(m) = 2 for m = 15, 21, 26, 57, 62, 85, 86, ... with 15 = 1111_2 = 33_4.
%e A326387 tau(m) = 8 and beta(m) = 4 for m = 40 = 1111_3 = 55_7 = 44_9 = 22_19.
%e A326387 tau(m) = 10 and beta(m) = 5 for m = 80 = 2222_3 = 88_9 = 55_15 = 44_19 = 22_39.
%o A326387 (PARI) isoblong(n) = my(m=sqrtint(n)); m*(m+1)==n; \\ A002378
%o A326387 beta(n) = sum(i=2, n-2, #vecsort(digits(n, i), , 8)==1); \\ A220136
%o A326387 isok(m) = !isprime(m) && !isoblong(m) && (beta(m) == numdiv(m)/2); \\ _Michel Marcus_, Jul 15 2019
%Y A326387 Cf. A000005 (tau), A220136 (beta).
%Y A326387 Subsequence of A167782, A308874 and A326380.
%Y A326387 Cf. A326386 (non-oblongs with tau(m)/2 - 1), A326388 (non-oblongs with tau(m)/2 + 1), A326389 (non-oblongs with tau(m)/2 + 2).
%K A326387 nonn,base
%O A326387 1,1
%A A326387 _Bernard Schott_, Jul 14 2019