A117182 a(n) = A117181(n) - A117180(n).

0, 0, 0, 1, 0, 7, 1, 5, 0, 0, 3, 0, 5, 3, 7, 4, 13, 0, 23, 9, 25, 1, 2, 2, 0, 13, 1, 22, 15, 11, 0, 4, 3, 7, 19, 29, 47, 2, 21, 5, 23, 9, 25, 4, 5, 0, 27, 0, 7, 0, 8, 22, 9, 3, 7, 46, 33, 23, 11, 8, 10, 27, 79, 37, 5, 0, 10, 39, 18, 5, 5, 15, 43, 20, 61, 45, 9, 17, 14, 14, 3, 49, 19, 7, 25, 16, 16

Offset

1,6

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. 3 is the smallest prime power dividing 12. So a(4) = 4 - 3 = 1.

Maple

A013929 := proc(nmax) local a, n ; a := [] ; n :=1 ; while nops(a) < nmax do if not numtheory[issqrfree](n) then a := [op(a), n] ; fi ; n := n+1 ; od ; a ; end :
A034699 := proc(n) local ifs, res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1, op(i, ifs))^op(2, op(i, ifs)), i=1..nops(ifs)) ; max(%) ; fi ; end:
A034684 := proc(n) local ifs, res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1, op(i, ifs))^op(2, op(i, ifs)), i=1..nops(ifs)) ; min(%) ; fi ; end:
a013929 := A013929(200) : for n from 1 to nops(a013929) do printf("%d, ", A034699(op(n, a013929))-A034684(op(n, a013929))) ; od ; # R. J. Mathar, May 10 2007

Mathematica

s[n_] := Differences[MinMax[Power @@@ FactorInteger[n]]][[1]]; s /@ Select[Range[250], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)

Crossrefs

Cf. A117180, A117181.

Sequence in context: A086210 A085467 A186168 * A143301 A225459 A317847

Adjacent sequences: A117179 A117180 A117181 * A117183 A117184 A117185

Keyword

nonn

Author

Leroy Quet, Mar 01 2006

Extensions

More terms from R. J. Mathar, May 10 2007

Status

approved