A326387 Non-oblong composites 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.

15, 21, 26, 40, 57, 62, 80, 85, 86, 91, 93, 111, 114, 124, 129, 133, 146, 170, 171, 172, 183, 215, 219, 222, 228, 242, 259, 266, 285, 292, 312, 314, 333, 341, 343, 365, 366, 381, 399, 422, 438, 444, 455, 468, 471, 482, 507, 518, 532, 549, 553

Offset

1,1

Comments

As tau(m) = 2 * 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 A326380: non-oblong composites which have only one Brazilian representation with three digits or more.

Links

Table of n, a(n) for n=1..51.

Index entries for sequences related to Brazilian numbers

Example

tau(m) = 4 and beta(m) = 2 for m = 15, 21, 26, 57, 62, 85, 86, ... with 15 = 1111_2 = 33_4.
tau(m) = 8 and beta(m) = 4 for m = 40 = 1111_3 = 55_7 = 44_9 = 22_19.
tau(m) = 10 and beta(m) = 5 for m = 80 = 2222_3 = 88_9 = 55_15 = 44_19 = 22_39.

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); \\ Michel Marcus, Jul 15 2019

Crossrefs

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

Subsequence of A167782, A308874 and A326380.

Cf. A326386 (non-oblongs with tau(m)/2 - 1), A326388 (non-oblongs with tau(m)/2 + 1), A326389 (non-oblongs with tau(m)/2 + 2).

Sequence in context: A057489 A070811 A211375 * A217078 A138594 A131651

Adjacent sequences: A326384 A326385 A326386 * A326388 A326389 A326390

Keyword

nonn,base

Author

Bernard Schott, Jul 14 2019

Status

approved