A076500 - OEIS

%I #8 Jun 24 2014 01:08:32

%S 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,

%T 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,

%U 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

%N Distance between 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 sequence A076450 if its sculpture is not equal to the sculpture of any smaller number. This sequence contains the first differences of A076450.

%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/sculptures/sculptures.htm">Sculptures</a>

%e 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.

%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]]]; Drop[nlist, 1]-Drop[nlist, -1]

%Y Cf. A076450.

%K nonn

%O 1,2

%A _Jon Perry_, Nov 08 2002

%E Edited by _Dean Hickerson_, Nov 18 2002