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

1,4

Links

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

Formula

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

Prog

(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");

Crossrefs

Cf. A001065, A051953, A291765.

Sequence in context: A341866 A300242 A293892 * A329035 A082904 A034868

Adjacent sequences: A295882 A295883 A295884 * A295886 A295887 A295888

Keyword

nonn

Author

Antti Karttunen, Dec 03 2017

Status

approved