A300245 Filter sequence combining arithmetic derivative (A003415) with its Möbius transform (A300251).
1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 11, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 27, 39, 40, 41, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 40, 60, 61, 62, 2, 63, 36, 64, 65, 66
Offset: 1
Keywords
Examples
a(16) = a(28) (= 11) because both A003415(16) = A003415(28) = 32 and A300251(16) = A300251(28) = 20.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
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PARI
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; }; write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); } A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415 A300251(n) = sumdiv(n,d,moebius(n/d)*A003415(d)); Aux300245(n) = [A003415(n), A300251(n)]; write_to_bfile(1,rgs_transform(vector(65537,n,Aux300245(n))),"b300245.txt");
Comments