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 A038199 Row sums of triangle T(m,n) = number of solutions to 1 <= a(1)
 1, 2, 6, 12, 30, 54, 126, 240, 504, 990, 2046, 4020, 8190, 16254, 32730, 65280, 131070, 261576, 524286, 1047540, 2097018, 4192254, 8388606, 16772880, 33554400, 67100670, 134217216, 268419060, 536870910, 1073708010, 2147483646 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The function T(m,n) described above has an inverse: see A038200. Also, Moebius transform of 2^n - 1 = A000225. Also, number of rationals in [0, 1) whose binary expansions consist just of repeating bits of (least) period exactly n (i.e., there's no preperiodic part), where 0 = 0.000... is considered to have period 1. - Brad Chalfan (brad(AT)chalfan.net), May 29 2006 REFERENCES Temba Shonhiwa, A Generalization of the Euler and Jordan Totient Functions, Fib. Quart., 37 (1999), 67-76. LINKS _Reinhard Zumkeller_, Table of n, a(n) for n = 1..1000 FORMULA a(n) = Sum mu(n/d)(2^d-1), d divides n. - Paul Barry, Mar 20 2005 MATHEMATICA Table[Plus@@((2^Divisors[n]-1)MoebiusMu[n/Divisors[n]]), {n, 1, 31}] - Brad Chalfan (brad(AT)chalfan.net), May 29 2006 PROG (Haskell) a038199 n = sum [a008683 (n `div` d) * (a000225 d)| d <- a027750_row n] -- Reinhard Zumkeller, Feb 17 2013 CROSSREFS A027375, A038199 and A056267 are all essentially the same sequence with different initial terms. Cf. A038200, A020921, A023995. Cf. A000225. Cf. A008683, A027750, A130887. Sequence in context: A224532 A179674 * A056267 A133996 A080742 A005417 Adjacent sequences:  A038196 A038197 A038198 * A038200 A038201 A038202 KEYWORD nonn,easy,nice AUTHOR Temba Shonhiwa (Temba(AT)maths.uz.ac.zw) EXTENSIONS Better description from Michael Somos More terms from Naohiro Nomoto, Sep 10 2001 More terms from Brad Chalfan (brad(AT)chalfan.net), May 29 2006 STATUS approved

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