A295880 Filter combining the number of divisors (A000005) and the sum of divisors (A000203) of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 44, 49, 50, 51, 44, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 57, 61, 64, 65, 66, 67, 68, 69, 57, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 79

Offset

1,2

Links

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

Formula

Restricted growth sequence transform of a(n) = (1/2)*(2 + ((A000005(n) + A000203(n))^2) - A000005(n) - 3*A000203(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])); }
A000005(n) = numdiv(n);
A000203(n) = sigma(n);
Anotsubmitted0(n) = (1/2)*(2 + ((A000005(n)+A000203(n))^2) - A000005(n) - 3*A000203(n));
write_to_bfile(1, rgs_transform(vector(up_to, n, Anotsubmitted0(n))), "b295880.txt");

Crossrefs

Cf. A000005, A000203, A295300, A295888.

Sequence in context: A293704 A322021 A295888 * A296090 A323372 A295300

Adjacent sequences: A295877 A295878 A295879 * A295881 A295882 A295883

Keyword

nonn

Author

Antti Karttunen, Dec 03 2017

Status

approved