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

Author

Antti Karttunen, Dec 07 2017

Keywords

• nonn

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

Crossrefs

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

Programs

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");