A326384 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.

42, 156, 182, 342, 1406, 1640, 6162, 7140, 14280, 14762, 20880, 25440, 29412, 32942, 33306, 47742, 48620, 49952, 61256, 67860, 95172, 95790, 158802, 176820, 191406, 202950, 209306, 257556, 296480, 297570

Offset

1,1

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 A326379: oblong numbers that have only one Brazilian representation with three digits or more.

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

Links

Table of n, a(n) for n=1..30.

Index entries for sequences related to Brazilian numbers

Example

There are two types of such numbers:
1) m is repunit with 3 digits or more in only one base:
156 = 12 * 13 = 1111_5 = 66_25 = 44_38 = 33_51 = 22_77 with tau(156) = 12 and beta(156) = 5.
2) m is repdigit with 3 digits or more and digit >= 2 in only one base:
tau(m) = 8 and beta(m) = 3:  42 = 6*7 = 222_4 = 33_13 = 22_20,
tau(m) = 12 and beta(m)= 5:  342 = 18*19 = 666_7 = 99_37 = 66_56 = 33_113 = 22_170,
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.

Crossrefs

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

Subsequence of A002378 (oblong numbers) and of A167782.

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

Sequence in context: A350579 A075289 A193571 * A263285 A263300 A299889

Adjacent sequences: A326381 A326382 A326383 * A326385 A326386 A326387

Keyword

nonn,base

Author

Bernard Schott, Jul 10 2019

Status

approved