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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jul 14 2019
STATUS
approved

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Last modified July 13 15:08 EDT 2024. Contains 374284 sequences. (Running on oeis4.)