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A076500
Distance between natural sculptures.
1
1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 6, 2, 2, 2, 4, 2, 2, 4, 2, 4, 6, 4, 2, 2, 2, 2, 2, 1, 5, 4, 4, 2, 6, 4, 2, 6, 2, 10, 8, 2, 2, 2, 1, 1, 2, 2, 4, 4, 2, 4, 2, 4, 2, 6, 8, 4, 12, 4, 2, 2, 10, 6, 8, 1, 13, 2, 6, 4, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 6, 2, 2, 4, 2, 4, 6, 2, 12, 4, 6, 6, 6, 8, 2, 5, 3, 24, 8, 4, 4
OFFSET
1,2
COMMENTS
The 'sculpture' of a positive integer n is the infinite vector (c[1], c[2], ...), where c[k] is the number of prime factors p of n (counted with multiplicity) such that n^(1/(k+1)) < p <= n^(1/k). A number is in sequence A076450 if its sculpture is not equal to the sculpture of any smaller number. This sequence contains the first differences of A076450.
EXAMPLE
The first 8 terms of A076450 are 1,2,4,6,8,10,12,16, so a(1)=1, a(2)=...=a(6)=2 and a(7)=4.
MATHEMATICA
sculpt[1]={}; sculpt[n_] := Module[{fn, v, i}, fn=FactorInteger[n]; v=Table[0, {Floor[Log[fn[[1, 1]], n]]}]; For[i=1, i<=Length[fn], i++, v[[Floor[Log[fn[[i, 1]], n]]]]+=fn[[i, 2]]]; v]; For[n=1; nlist=slist={}, n<500, n++, sn=sculpt[n]; If[ !MemberQ[slist, sn], AppendTo[slist, sn]; AppendTo[nlist, n]]]; Drop[nlist, 1]-Drop[nlist, -1]
CROSSREFS
Cf. A076450.
Sequence in context: A125918 A239202 A083533 * A344887 A060594 A327813
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 08 2002
EXTENSIONS
Edited by Dean Hickerson, Nov 18 2002
STATUS
approved