A141574 - OEIS

%I #5 Mar 30 2012 18:52:27

%S 3,5,7,5,9,4,6,7,13,5,15,10,7,4,19,5,22,4,8,9,34,4,5,10,15,6,5,9,31,8,

%T 33,4,4,14,19,12,4,6,39,22,15,4,46,5,50,4,14,8,25,49,4,5,14,7,8,19,15,

%U 55,6,8,13,4,10,21,88,4,8,63,34,10,4,4,4,18,5,78,4,20,25,12,73,4,6,75

%N Sums of pairs of the infinite list generated by the flat list of the factorizations of all integers.

%C Factorize n to its full extent into the list 1, 2, 3, 2*2, 5, 2*3, 7, 2*2*2, 3*3, 2*5, 11, 2*2*3,..

%C Remove delimiting commas and the multiplication signs and build new sums by pairing consecutive pairs of numbers of this list, 1+2, 3+2, 2+5, 2+3, 7+2, 2+2, 3+3, 2+5, 11+2, 2+3.. to construct the sequence.

%p pflat := proc(nmax) local a,ifs,n,p,c ; a := [1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do q := op(1,p) ; for c from 1 to op(2,p) do a := [op(a),q] ; od: od: od: a ; end: pL := pflat(90) : for n from 1 to nops(pL)-2 by 2 do printf("%d,", op(n,pL)+op(n+1,pL)) ; od: # _R. J. Mathar_, Aug 21 2008

%t f[n_] := Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n]; Plus @@@ Partition[ Flatten@ Array[f, 74], 2] (* _Robert G. Wilson v_, Aug 31 2008 *)

%Y Cf. A000040.

%K nonn,less

%O 1,1

%A _Juri-Stepan Gerasimov_, Aug 17 2008

%E Edited, corrected and extended by _R. J. Mathar_, Aug 21 2008