A076450 Natural sculptures.

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

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: A049225 A351910 A371177 * A097379 A371288 A114871

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