A077462 Prime factor configuration patterns.
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
Offset: 0
Examples
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
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.
Programs
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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 *) -
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])))))
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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
Comments