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A116512
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a(n) = number of positive integers each which is <= n and each which is divisible by exactly one prime dividing n (but is coprime to every other prime dividing n). a(1) = 0.
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3
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0, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 6, 8, 1, 9, 1, 10, 8, 11, 1, 12, 5, 13, 9, 14, 1, 14, 1, 16, 12, 17, 10, 18, 1, 19, 14, 20, 1, 20, 1, 22, 18, 23, 1, 24, 7, 25, 18, 26, 1, 27, 14, 28, 20, 29, 1, 28, 1, 31, 24, 32, 16, 32, 1, 34, 24, 34, 1, 36, 1, 37, 30, 38, 16, 38, 1, 40, 27, 41, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) = number of m's, 1 <= m <= n, where GCD(m,n) is a power of a prime (>1).
We could also have taken a(1) = 1, but a(1) = 0 is better since there are no numbers <= 1 with the desired property. - N. J. A. Sloane (njas(AT)research.att.com), Sep 16 2006
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EXAMPLE
| 12 is divisible by 2 and 3. The positive integers which are <= 12 and which are divisible by 2 or 3, but not by both 2 and 3, are: 2,3,4,8,9,10. Since there are six such integers, a(12) = 6.
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MAPLE
| with(numtheory): a:=proc(n) local c, j: c:=0: for j from 1 to n do if nops(factorset(gcd(j, n)))=1 then c:=c+1 else c:=c: fi od: c; end: seq(a(n), n=1..90); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2006
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MATHEMATICA
| Table[Length@Select[GCD[n, Range@n], MatchQ[FactorInteger@#, {{_, _}}]&], {n, 93}] - Giovanni Resta (g.resta(AT)iit.cnr.it), Apr 04 2006
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PROG
| (PARI) { for(n=1, 60, hav=0; for(i=1, n, g = gcd(i, n); d = factor(g); dec=matsize(d); if( dec[1] == 1, hav++; ); ); print1(hav, ", "); ); } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 29 2006
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CROSSREFS
| Cf. A119790, A119794, A120499.
Sequence in context: A159353 A032742 A060654 * A075388 A036445 A098910
Adjacent sequences: A116509 A116510 A116511 * A116513 A116514 A116515
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Mar 23 2006
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Emeric Deutsch (deutsch(AT)duke.poly.edu) and Giovanni Resta (g.resta(AT)iit.cnr.it), Apr 01 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 16 2006
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