A318887 Filter sequence related to the differences of prime factors of n.

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

Offset: 1

Author

Antti Karttunen, Sep 24 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A318885.

Links

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

Crossrefs

Cf. A318885, A318888.

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; };
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));
v318887 = rgs_transform(vector(up_to,n,A318885(n)));
A318887(n) = v318887[n];