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Search: id:A100347
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| A100347 |
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Number of compositions of n into parts all relatively prime to n. |
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+0
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| 1, 1, 3, 3, 15, 3, 63, 21, 125, 36, 1023, 25, 4095, 314, 3357, 987, 65535, 207, 262143, 2782, 164498, 17114, 4194303, 1705, 11349545, 119620, 7256527, 209376, 268435455, 1261, 1073741823, 2178309, 276465135, 5687872, 8460492865, 114575
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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Coefficient of x^n in expansion of 1/(1-Sum_{d : gcd(d, n)=1} x^d ).
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EXAMPLE
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a(4)=3 because among the eight compositions of 4 (namely, 1111, 112, 121, 211, 22, 13, 31, and 4) only 1111, 13, and 31 have parts all relatively prime to 4.
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MAPLE
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RP:=proc(n) local A, j: A:={}: for j from 1 to n do if gcd(j, n)=1 then A:=A union {j} else A:=A: fi od: end: a:=proc(n) local S, j, ser: S:=1/(1-sum(x^RP(n)[j], j=1..nops(RP(n)))): ser:=series(S, x=0, n+5): coeff(ser, x^n): end: seq(a(n), n=1..40); (Deutsch)
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CROSSREFS
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Cf. A057562.
Sequence in context: A094152 A131943 A100371 this_sequence A114320 A086116 A100735
Adjacent sequences: A100344 A100345 A100346 this_sequence A100348 A100349 A100350
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 29 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 25 2005
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