A302046 A filter sequence analogous to A101296 for nonstandard factorization based on the sieve of Eratosthenes (A083221).

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 6, 2, 6, 5, 4, 2, 8, 3, 4, 4, 6, 2, 9, 2, 10, 6, 4, 4, 11, 2, 4, 4, 8, 2, 8, 2, 6, 7, 4, 2, 12, 3, 6, 6, 6, 2, 9, 5, 8, 6, 4, 2, 13, 2, 4, 4, 14, 4, 13, 2, 6, 8, 9, 2, 15, 2, 4, 4, 6, 4, 9, 2, 12, 6, 4, 2, 15, 6, 4, 9, 8, 2, 12, 5, 6, 10, 4, 4, 16, 2, 6, 4, 11, 2, 13, 2, 8, 11

Offset: 1

Author

Antti Karttunen, Mar 31 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A278524.

See A302042 for the description of the nonstandard factorization employed here.

For all i, j:

a(i) = a(j) => A253557(i) = A253557(j).

a(i) = a(j) => A302041(i) = A302041(j).

a(i) = a(j) => A302050(i) = A302050(j).

a(i) = a(j) => A302051(i) = A302051(j) => A302052(i) = A302052(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences generated by sieves

Crossrefs

Cf. A101296, A250246, A278524, A302042, A302044, A302045.

Programs

PARI

up_to = 32769;
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])); }
A020639(n) = { if(1==n,n,vecmin(factor(n)[, 1])); };
A078898(n) = { if(n<=1,n, my(spf=A020639(n),k=1,m=n/spf); while(m>1,if(A020639(m)>=spf,k++); m--); (k)); };
A001511(n) = 1+valuation(n,2);
A302045(n) = A001511(A078898(n));
A302044(n) = if(1==n,n,my(k=0); while((n%2), n = A268674(n); k++); n = (n/2^valuation(n, 2)); while(k>0, n = A250469(n); k--); (n));
A302041(n) = if(1==n, 0,1+A302041(A302044(n)));
Aux302046(n) = if(1==n,n, my(k=A302041(n), v = vector(k),i=1); while(n>1,v[i] = A302045(n); n = A302044(n); i++); vecsort(v));
write_to_bfile(1,rgs_transform(vector(up_to,n,Aux302046(n))),"b302046.txt");