A326386 Non-oblong composites 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.

8, 10, 14, 18, 22, 24, 27, 28, 32, 33, 34, 35, 38, 39, 44, 45, 46, 48, 50, 51, 52, 54, 55, 58, 60, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 82, 84, 87, 88, 92, 94, 95, 96, 98, 99, 102, 104, 105, 106, 108, 112, 115, 116, 117, 118, 119, 120, 122, 123, 125, 126, 128, 130, 134, 135, 136

Offset

1,1

Comments

As tau(m) = 2 * (1 + beta(m)), the terms of this sequence are not squares.

The number of Brazilian representations of a non-oblong number m with repdigits of length = 2 is beta'(n) = tau(n)/2 - 1.

This sequence is the first subsequence of A326379: non-oblong composites which have no Brazilian representation with three digits or more.

Links

Table of n, a(n) for n=1..66.

Bernard Schott, beta = f(tau) - Abstract

Index entries for sequences related to Brazilian numbers

Example

tau(m) = 4 and beta(m)=1 for m = 8, 10, 14, 22, 27, 33, 34, 35, 38, ... 8 = 22_3,
tau(m) = 6 and beta(m)=2 for m = 18, 28, 32, 44, 45, 50, ... 18 = 33_5 = 22_8,
tau(m) = 8 and beta(m)=3 for m = 24, 54, 66, 70, ... 24 = 44_5 = 33_7 = 22_11,
tau(m) = 10 and beta(m) = 4: 48, 112, ... 48 = 66_7 = 44_11 = 33_15 = 22_23.

Prog

(PARI) isoblong(n) = my(m=sqrtint(n)); m*(m+1)==n; \\ A002378
beta(n) = sum(i=2, n-2, #vecsort(digits(n, i), , 8)==1); \\ A220136
isok(m) = !isprime(m) && !isoblong(m) && (beta(m) == numdiv(m)/2 - 1); \\ Michel Marcus, Jul 15 2019

Crossrefs

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

Subsequence of A308874 and of A326379.

Cf. A326387 (non-oblongs with tau(m)/2), A326388 (non-oblongs with tau(m)/2 + 1), A326389 (non-oblongs with tau(m)/2 + 2).

Sequence in context: A368280 A262708 A134321 * A027693 A196226 A250290

Adjacent sequences: A326383 A326384 A326385 * A326387 A326388 A326389

Keyword

nonn,base

Author

Bernard Schott, Jul 12 2019

Status

approved