login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326378 Numbers m such that beta(m) = tau(m)/2 - 2 where beta(m) is the number of Brazilian representations of m and tau(m) is the number of divisors of m. 10
6, 12, 20, 30, 56, 72, 90, 110, 132, 210, 240, 272, 306, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1482, 1560, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550, 2652, 2756, 2862, 2970, 3080, 3192, 3306, 3422, 3540, 3660, 3782 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

As tau(m) = 2 * (2 + beta(m)), the terms of this sequence are not squares. Indeed, there exists only one family that satisfies this relation and these integers are exactly the oblong numbers that have no Brazilian representation with three digits or more.

There are no integers such as beta(m) = tau(m)/2 - q with q >= 3.

LINKS

Table of n, a(n) for n=1..54.

Bernard Schott, Relation beta = f(tau)

Index entries for sequences related to Brazilian numbers

EXAMPLE

1) tau(m) = 4 and beta(m) = 0: m = 6 which is not Brazilian.

2) tau(m) = 6 and beta(m) = 1: m = 12, 20.

   12 = 3 * 4 = 22_5, 20 = 4 * 5 = 22_9.

3) tau(m) = 8 and beta(m) = 2: m = 30, 56, 110, 506, 2162, 3422, ...

   30 = 5 * 6 = 33_9 = 22_14, 56 = 7 * 8 = 44_13 = 22_27.

4) tau(m) = 10 and beta(m) = 3: m = 272, ...

   272 = 16 * 17 = 88_32 = 44_67 = 22_135.

5) tau(m) = 12 and beta(m) = 4: m = 72, 90, 132, 306, 380, 650, 812, 992, ...

   72 = 8 * 9 = 66_11 = 44_17 = 33_23 = 22_35.

PROG

(PARI) beta(n) = sum(i=2, n-2, #vecsort(digits(n, i), , 8)==1); \\ A220136

isok(n) = beta(n) == numdiv(n)/2 - 2; \\ Michel Marcus, Jul 08 2019

CROSSREFS

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

Subsequence of A002378 (oblong numbers).

Cf. A326379 (tau(m)/2 - 1), A326380 (tau(m)/2), A326381 (tau(m)/2 + 1), A326382 (tau(m)/2 + 2), A326383 (tau(m)/2 + 3).

Cf. A326384 (oblongs with tau(m)/2 - 1), A326385 (oblongs with tau(m)/2).

Sequence in context: A007622 A180291 A056930 * A064971 A130199 A295904

Adjacent sequences:  A326375 A326376 A326377 * A326379 A326380 A326381

KEYWORD

nonn,base

AUTHOR

Bernard Schott, Jul 02 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 09:09 EDT 2020. Contains 337380 sequences. (Running on oeis4.)