A140123 - OEIS

A140123

Denominator of Sum_{k=1..n} (-1)^k / semiprime(k).

4, 12, 36, 180, 1260, 252, 252, 2772, 69300, 900900, 900900, 15315300, 15315300, 290990700, 290990700, 6692786100, 46849502700, 46849502700, 46849502700, 46849502700, 1358635578300, 42117702927300, 42117702927300, 42117702927300

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

The first 10 values of A140122(n)/a(n) = -1/4, -1/12, -7/36, -17/180, -209/1260, -25/252, -37/252, -281/2772, -9797/69300, -92711/900900. The 10th term of the sum is (-1/4)+(1/6)-(1/9)+(1/10)-(1/14)+(1/15)-(1/21)+(1/22)-(1/25)+(1/26) = -92711/900900 hence a(10) = 900900. The 20th term of the alternating sum is (-1/4)+(1/6)-(1/9)+(1/10)-(1/14)+(1/15)-(1/21)+(1/22)-(1/25)+(1/26)-(1/33)+(1/34)-(1/35)+(1/38)-(1/39)+(1/46)-(1/49)+(1/51)-(1/55)+(1/57) = -5218865543/46849502700, hence a(20) = 46849502700.

MAPLE

A001358 := proc(n) local a; if n = 1 then 4; else for a from A001358(n-1)+1 do if numtheory[bigomega](a) = 2 then RETURN(a) ; fi ; od: fi ; end: A140123 := proc(n) local k ; denom(add ( (-1)^k/A001358(k), k=1..n)) ; end: seq(A140123(n), n=1..30) ; # R. J. Mathar, May 13 2008

CROSSREFS

Cf. A001358, A002110, A024530, A140122.

Sequence in context: A056383 A293857 A052643 * A164853 A076124 A247952

Adjacent sequences: A140120 A140121 A140122 * A140124 A140125 A140126

KEYWORD

easy,frac,nonn

AUTHOR

Jonathan Vos Post, May 09 2008

EXTENSIONS

More terms from R. J. Mathar, May 13 2008

STATUS

approved