A076500 Distance between natural sculptures.

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

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

Table of n, a(n) for n=1..102.

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 * A344887 A060594 A327813

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