A295885 Filter combining sum of proper divisors (A001065) and cototient (A051953) of n.

1, 1, 1, 2, 1, 3, 1, 4, 5, 6, 1, 7, 1, 8, 9, 10, 1, 11, 1, 12, 13, 14, 1, 15, 16, 17, 18, 19, 1, 20, 1, 21, 22, 23, 24, 25, 1, 26, 27, 28, 1, 29, 1, 30, 31, 32, 1, 33, 34, 35, 36, 37, 1, 38, 27, 39, 40, 41, 1, 42, 1, 43, 44, 45, 46, 47, 1, 48, 49, 50, 1, 51, 1, 52, 53, 54, 46, 55, 1, 56, 57, 58, 1, 59, 40, 60, 61, 62, 1, 63, 36

Offset: 1

Author

Antti Karttunen, Dec 03 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001065, A051953, A291765.

Programs

PARI

allocatemem(2^30);
up_to = 65537;
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])); }
A051953(n) = (n-eulerphi(n));
A001065(n) = (sigma(n)-n);
Anotsubmitted5(n) = (1/2)*(2 + ((A051953(n)+A001065(n))^2) - A051953(n) - 3*A001065(n));
write_to_bfile(1,rgs_transform(vector(up_to,n,Anotsubmitted5(n))),"b295885.txt");

Formula

Restricted growth sequence transform of a(n) = (1/2)*(2 + ((A051953(n) + A001065(n))^2) - A051953(n) - 3*A001065(n)).