cp's OEIS Frontend

A326385 Oblong numbers 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 A326385 #16 Jul 20 2019 23:23:26
%S A326385 3906,37830,97656,132860,1206702,2441406,6034392,10761680,21441530,
%T A326385 96855122,148705830,203932680,322866992,747612306,871696100,
%U A326385 1187526060,1525878906,1743939360,2075941406,3460321800,5541090282,8574111812,9455714840,12880093590,18854722656
%N A326385 Oblong numbers 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 A326385 The number of Brazilian representations of an oblong number m with repdigits of length = 2 is beta'(n) = tau(n)/2 -  2.
%C A326385 This sequence is the second subsequence of A326380: oblong numbers that have exactly two Brazilian representations with three digits or more.
%H A326385 Chai Wah Wu, <a href="/A326385/b326385.txt">Table of n, a(n) for n = 1..129</a>
%H A326385 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Br#Brazilian_numbers">Index entries for sequences related to Brazilian numbers</a>
%e A326385 3906 = 62 * 63 is oblong, tau(3906) = 24, beta(3906) = 12 with beta'(3906) = 10 and beta"(3906) = 2: 3906 = 111111_5 = 666_25 = (42,42)_92 = (31,31)_125 = (21,21)_185 = (18,18)_216 = (14,14)_278 = 99_433 = 77_557 = 66_650 = 33_130 = 22_1952.
%Y A326385 Cf. A000005 (tau), A220136 (beta).
%Y A326385 Subsequence of A002378 (oblong numbers) and of A167783.
%Y A326385 Cf. A326378 (oblongs with tau(m)/2 - 2), A326384 (oblongs with tau(m)/2 - 1), A309062 (oblongs with tau(m)/2 + k, k >= 1).
%K A326385 nonn,base
%O A326385 1,1
%A A326385 _Bernard Schott_, Jul 10 2019
%E A326385 a(6)-a(25) from _Giovanni Resta_, Jul 11 2019