A326384 - OEIS

%I #25 May 24 2022 02:48:06

%S 42,156,182,342,1406,1640,6162,7140,14280,14762,20880,25440,29412,

%T 32942,33306,47742,48620,49952,61256,67860,95172,95790,158802,176820,

%U 191406,202950,209306,257556,296480,297570

%N Oblong composite numbers m such that beta(m) = tau(m)/2 - 1 where beta(m) is the number of Brazilian representations of m and tau(m) is the number of divisors of m.

%C The number of Brazilian representations of an oblong number m with repdigits of length = 2 is beta'(n) = tau(n)/2 - 2.

%C This sequence is the second subsequence of A326379: oblong numbers that have only one Brazilian representation with three digits or more.

%C Prime 2 is oblong and satisfies also beta(2) = tau(2)/2 - 1 = 0 but non-Brazilian primes are in A220627.

%H <a href="/index/Br#Brazilian_numbers">Index entries for sequences related to Brazilian numbers</a>

%e There are two types of such numbers:

%e 1) m is repunit with 3 digits or more in only one base:

%e 156 = 12 * 13 = 1111_5 = 66_25 = 44_38 = 33_51 = 22_77 with tau(156) = 12 and beta(156) = 5.

%e 2) m is repdigit with 3 digits or more and digit >= 2 in only one base:

%e tau(m) = 8 and beta(m) = 3:  42 = 6*7 = 222_4 = 33_13 = 22_20,

%e tau(m) = 12 and beta(m)= 5:  342 = 18*19 = 666_7 = 99_37 = 66_56 = 33_113 = 22_170,

%e tau(m) = 16 and beta(m)= 7: 1640 = 40*41 = 2222_9 = (20,20)_81 = (10,10)_2 = 88_204 = 55_327 = 44_409 = 22_819.

%Y Cf. A000005 (tau), A220136 (beta).

%Y Subsequence of A002378 (oblong numbers) and of A167782.

%Y Cf. A326378 (oblongs with tau(m)/2 - 2), A326385 (oblongs with tau(m)/2), A309062 (oblongs with tau(m)/2 + k, k >= 1).

%K nonn,base

%O 1,1

%A _Bernard Schott_, Jul 10 2019