A296089 Filter combining the sum of divisors (A000203) and 2-adic valuation of n (A007814); restricted growth sequence transform of A286460.

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

Offset

1,2

Comments

This seems to be also the restricted growth sequence transform of A286359.

For all i, j:

a(i) = a(j) => A296088(i) = A296088(j).

Links

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

Prog

(PARI)
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])); }
A000203(n) = sigma(n);
A001511(n) = (1+valuation(n, 2));
A286460(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n));
write_to_bfile(1, rgs_transform(vector(up_to, n, A286460(n))), "b296089.txt");

Crossrefs

Cf. A000203, A007814, A286359, A286460, A296088, A296090.

Sequence in context: A369261 A369260 A296088 * A323368 A369259 A080686

Adjacent sequences: A296086 A296087 A296088 * A296090 A296091 A296092

Keyword

nonn

Author

Antti Karttunen, Dec 07 2017

Status

approved