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A302046 A filter sequence analogous to A101296 for nonstandard factorization based on the sieve of Eratosthenes (A083221). 3
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 (list; graph; refs; listen; history; text; internal format)
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 A290110 A300250

Adjacent sequences:  A302043 A302044 A302045 * A302047 A302048 A302049

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 31 2018

STATUS

approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)