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

Author

Jonathan Vos Post, Jun 09 2011

Keywords

• nonn
• easy
• frac

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.

Examples

			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.
		

Crossrefs

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

Programs

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 *)

PARI

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