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A038199
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Row sums of triangle T(m,n) = number of solutions to 1 <= a(1)<a(2)<...<a(m) <= n, where gcd( a(1), a(2), ....a(m), n)=1, in A020921.
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9
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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Temba Shonhiwa, A Generalization of the Euler and Jordan Totient Functions, Fib. Quart., 37 (1999), 67-76.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = Sum mu(n/d)(2^d-1), d divides n. - Paul Barry, Mar 20 2005
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MATHEMATICA
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Table[Plus@@((2^Divisors[n]-1)MoebiusMu[n/Divisors[n]]), {n, 1, 31}] - Brad Chalfan (brad(AT)chalfan.net), May 29 2006
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PROG
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(Haskell)
a038199 n = sum [a008683 (n `div` d) * (a000225 d)| d <- a027750_row n]
-- Reinhard Zumkeller, Feb 17 2013
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CROSSREFS
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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
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Temba Shonhiwa (Temba(AT)maths.uz.ac.zw)
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EXTENSIONS
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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
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STATUS
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approved
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