A318888 Filter sequence combining the 2-adic valuation of n (A007814) with the differences between odd primes in the prime factorization of n.

1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 9, 10, 3, 11, 3, 8, 12, 5, 3, 13, 7, 5, 14, 8, 3, 15, 3, 16, 17, 5, 9, 18, 3, 5, 19, 13, 3, 20, 3, 8, 21, 5, 3, 22, 7, 11, 23, 8, 3, 24, 25, 13, 26, 5, 3, 27, 3, 5, 28, 29, 17, 30, 3, 8, 31, 15, 3, 32, 3, 5, 33, 8, 12, 34, 3, 22, 35, 5, 3, 36, 37, 5, 38, 13, 3, 39, 25, 8, 40, 5, 23, 41, 3, 11, 42, 18, 3, 43, 3, 13, 44

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of an ordered pair [A007814(n), A318885(A000265(n))].

For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A305891(i) = A305891(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A305801, A305891, A318500, A318885, A318887.

Programs

PARI

up_to = 100000;
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; };
A000265(n) = (n/2^valuation(n, 2));
A007814(n) = valuation(n,2);
A318885(n) = if(1==n,n,my(f=factor(n),m=2^f[1,2],i=1); for(k=2,#f~,i += (f[k,1]-f[k-1,1]); m *= prime(i)^f[k,2]); (m));
v318888 = rgs_transform(vector(up_to,n,[A007814(n), A318885(A000265(n))]));
A318888(n) = v318888[n];