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Search: id:A076500
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| A076500 |
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Distance between natural sculptures. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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Jon Perry, Sculptures
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EXAMPLE
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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.
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A076450.
Sequence in context: A060467 A125918 A083533 this_sequence A060594 A104361 A086876
Adjacent sequences: A076497 A076498 A076499 this_sequence A076501 A076502 A076503
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Nov 08 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Nov 18 2002
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