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 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 Bernard Schott, Relation beta = f(tau) 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

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