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.

3906, 37830, 97656, 132860, 1206702, 2441406, 6034392, 10761680, 21441530, 96855122, 148705830, 203932680, 322866992, 747612306, 871696100, 1187526060, 1525878906, 1743939360, 2075941406, 3460321800, 5541090282, 8574111812, 9455714840, 12880093590, 18854722656

Offset: 1

Author

Bernard Schott, Jul 10 2019

Keywords

• nonn
• base

Comments

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

This sequence is the second subsequence of A326380: oblong numbers that have exactly two Brazilian representations with three digits or more.

Examples

			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.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..129
• Index entries for sequences related to Brazilian numbers

Crossrefs

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

Subsequence of A002378 (oblong numbers) and of A167783.

Cf. A326378 (oblongs with tau(m)/2 - 2), A326384 (oblongs with tau(m)/2 - 1), A309062 (oblongs with tau(m)/2 + k, k >= 1).

Extensions

a(6)-a(25) from Giovanni Resta, Jul 11 2019