A191645 Numerators of the n-th partial "harmonic" sum of 1 + inverse semiprimes.

5, 17, 55, 293, 2141, 445, 457, 5153, 131597, 1745411, 1772711, 30586537, 31024117, 597115873, 604577173, 14050770329, 99311504603, 100230122303, 101081931443, 101903852543

Offset

1,1

Comments

Denominators appear to be the same as A140123. The fractions begin: 5/4, 17/12, 55/36, 293/180, 2141/1260, 445/252, 457/252, 5153/2772, 131597/69300, ...

This is the semiprime analog of A024528.

Links

Table of n, a(n) for n=1..20.

Example

a(1) =  5 because 1 + 1/4 = 5/4.
a(2) = 17 because 1 + 1/4 + 1/6 = 17/12.
a(3) = 55 because 1 + 1/4 + 1/6 + 1/9 = 55/36.

Maple

A191645 := proc(n) 1+add(1/A001358(i), i=1..n) ; numer(%) ; end proc:
seq(A191645(n), n=1..20) ; # R. J. Mathar, Jun 16 2011

Mathematica

With[{sp=Join[{1}, Select[Range[100], PrimeOmega[#]==2&]]}, Rest[ Numerator[ Accumulate[1/sp]]]] (* Harvey P. Dale, May 01 2015 *)

Prog

(PARI) s=1; for(k=1, 99, bigomega(k)==2 & print1(numerator(s+=1/k)", "))  \\ M. F. Hasler, Jun 17 2011

Crossrefs

Cf. A001358, A112141, A001008, A140123, A024528.

Sequence in context: A183712 A244235 A081495 * A146240 A112410 A146271

Adjacent sequences: A191642 A191643 A191644 * A191646 A191647 A191648

Keyword

nonn,easy,frac

Author

Jonathan Vos Post, Jun 09 2011

Status

approved