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

1,2

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

Prog

(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");

Crossrefs

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

Sequence in context: A101296 A305898 A181819 * A077462 A324203 A290110

Adjacent sequences: A302043 A302044 A302045 * A302047 A302048 A302049

Keyword

nonn

Author

Antti Karttunen, Mar 31 2018

Status

approved