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%I #7 Jun 24 2014 01:08:32
%S 1,2,4,6,8,10,12,16,18,20,22,24,30,32,34,36,40,42,44,48,50,54,60,64,
%T 66,68,70,72,74,75,80,84,88,90,96,100,102,108,110,120,128,130,132,134,
%U 135,136,138,140,144,148,150,154,156,160,162,168,176,180,192,196,198,200
%N Natural sculptures.
%C 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 the sequence if its sculpture is not equal to the sculpture of any smaller number.
%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/sculptures/sculptures.htm">Sculptures</a>
%t 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]]]; nlist
%Y The first differences are in A076500.
%K nonn
%O 1,2
%A _Jon Perry_, Nov 07 2002
%E Edited by _Dean Hickerson_, Nov 18 2002
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