A300241 Filter sequence combining A001065(n) and A009195(n), the sum of proper divisors of n and gcd(n,phi(n)).

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, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 40, 41, 42, 43, 2, 44, 2, 45, 46, 47, 48, 49, 2, 50, 51, 52, 2, 53, 2, 54, 55, 56, 48, 57, 2, 58, 59, 60, 2, 61, 62, 63, 64, 65, 2, 66, 37, 67, 68, 69, 70, 71, 2, 72, 73

Offset

1,2

Comments

Restricted growth sequence transform of P(A001065(n), A009195(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

Links

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

Example

a(65) = a(77) (= 48) because A001065(65) = A001065(77) = 19 and A009195(65) = A009195(77) = 1.

Prog

(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])); }
A001065(n) = (sigma(n)-n);
A009195(n) = gcd(n, eulerphi(n));
Aux300241(n) = (1/2)*(2 + ((A001065(n)+A009195(n))^2) - A001065(n) - 3*A009195(n));
write_to_bfile(1, rgs_transform(vector(65537, n, Aux300241(n))), "b300241.txt");

Crossrefs

Cf. A001065, A009195.

Cf. also A300231, A300240, A300242, A300243.

Sequence in context: A300833 A373150 A300243 * A320014 A319693 A296073

Adjacent sequences: A300238 A300239 A300240 * A300242 A300243 A300244

Keyword

nonn

Author

Antti Karttunen, Mar 02 2018

Status

approved