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

1,2

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

Prog

(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];

Crossrefs

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

Sequence in context: A319337 A305891 A319347 * A323079 A331174 A355836

Adjacent sequences: A318885 A318886 A318887 * A318889 A318890 A318891

Keyword

nonn

Author

Antti Karttunen, Sep 24 2018

Status

approved