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A077462 Prime factor configuration patterns. 8
0, 1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 8, 2, 6, 4, 4, 2, 9, 3, 4, 5, 6, 2, 10, 2, 11, 4, 4, 4, 12, 2, 4, 4, 9, 2, 10, 2, 6, 6, 4, 2, 13, 3, 8, 4, 6, 2, 14, 4, 9, 4, 4, 2, 15, 2, 4, 6, 16, 4, 10, 2, 6, 4, 10, 2, 17, 2, 4, 8, 6, 4, 10, 2, 13, 7, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Call two numbers equivalent if they have the same prime factorization exponents (in the same order). This sequence enumerates the equivalence classes.

A055932(a(n)) = A071364(n). - David Wasserman, Dec 21 2004

From Antti Karttunen, Jun 13 2018: (Start)

After a(0) = 0, this is the restricted growth sequence transform of A071364. The latter sequence is an "ordered variant" of A046523, and because A101296 is the rgs-transform of A046523, it follows that for all i, j: a(i) = a(j) => A101296(i) = A101296(j).

(End)

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..100000 (terms 0..10000 from T. D. Noe)

S. Whealton, Prime Factor Configuration Pattern Numbers.

EXAMPLE

12 = 2^2*3^1 has exponents {2,1}, and is the first number with that pattern, so its value is one more than the largest previous value; a(12) = 6. Contrast that with 18 = 2^1*3^2 having exponents {1,2}, which is different from {2,1}, so a(18) is not equal to a(12). - Franklin T. Adams-Watters, Aug 01 2012

MATHEMATICA

fList = {{0}}; Join[{0, 1}, Table[e = Transpose[FactorInteger[n]][[2]]; pos = Position[fList, e]; If[pos == {}, AppendTo[fList, e]; Length[fList], pos[[1, 1]]], {n, 2, 100}]] (* T. D. Noe, Aug 01 2012 *)

PROG

(PARI) a(n)=local(vn); if(n<1, return(0)); vn=factor(n)[, 2]; for(i=1, n, if(vn==factor(i)[, 2], return(#Set(vector(i, j, factor(j)[, 2])))))

(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; };

A071364(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = prime(i)); factorback(f); }; \\ From A071364

v077462 = rgs_transform(vector(up_to, n, A071364(n)));

A077462(n) = if(!n, n, v077462[n]); \\ Antti Karttunen, Jun 13 2018

CROSSREFS

Cf. A037916, A071364, A101296, A290110, A300250.

One more than A079616.

Sequence in context: A305898 A181819 A302046 * A324203 A290110 A300250

Adjacent sequences:  A077459 A077460 A077461 * A077463 A077464 A077465

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Nov 07 2002

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)