

A076450


Natural sculptures.


1



1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 30, 32, 34, 36, 40, 42, 44, 48, 50, 54, 60, 64, 66, 68, 70, 72, 74, 75, 80, 84, 88, 90, 96, 100, 102, 108, 110, 120, 128, 130, 132, 134, 135, 136, 138, 140, 144, 148, 150, 154, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200
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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 the sequence if its sculpture is not equal to the sculpture of any smaller number.


LINKS

Table of n, a(n) for n=1..62.
Jon Perry, Sculptures


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]]]; nlist


CROSSREFS

The first differences are in A076500.
Sequence in context: A002174 A002202 A049225 * A097379 A114871 A085150
Adjacent sequences: A076447 A076448 A076449 * A076451 A076452 A076453


KEYWORD

nonn


AUTHOR

Jon Perry, Nov 07 2002


EXTENSIONS

Edited by Dean Hickerson, Nov 18 2002


STATUS

approved



