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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Jon Perry, Sculptures 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 * A060594 A327813 A104361 Adjacent sequences:  A076497 A076498 A076499 * A076501 A076502 A076503 KEYWORD nonn AUTHOR Jon Perry, Nov 08 2002 EXTENSIONS Edited by Dean Hickerson, Nov 18 2002 STATUS approved

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)