A319346 Filter sequence combining the sum of proper divisors (A001065) with the 2-adic valuation of n (A007814).

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

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A001065(n), A007814(n)].

Links

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

Crossrefs

Cf. A001065, A007814, A305801, A319338.

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; };
A001065(n) = (sigma(n)-n);
A007814(n) = valuation(n,2);
v319346 = rgs_transform(vector(up_to,n,[A001065(n),A007814(n)]));
A319346(n) = v319346[n];