A074251 Sum of the squarefree numbers from the smallest prime factor of n to the largest prime factor of n.

0, 2, 3, 2, 5, 5, 7, 2, 3, 10, 11, 5, 13, 23, 8, 2, 17, 5, 19, 10, 21, 44, 23, 5, 5, 57, 3, 23, 29, 10, 31, 2, 42, 103, 18, 5, 37, 122, 55, 10, 41, 23, 43, 44, 8, 188, 47, 5, 7, 10, 101, 57, 53, 5, 39, 23, 120, 243, 59, 10, 61, 304, 21, 2, 52, 44, 67, 103, 186, 23, 71, 5, 73

Offset

1,2

Comments

a(p) = p for prime p. - Robert Israel, Jan 18 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(22) = 44 because 22 = 2*11 and the sum of squarefree numbers between 2 and 11 is 2 + 3 + 5 + 6 + 7 + 10 + 11 = 44.

Maple

with(numtheory): a:=proc(n) local nf, nnf, s, j: nf:=factorset(n): nnf:=nops(nf): s:=0: for j from nf[1] to nf[nnf] do if abs(mobius(j))>0 then s:=s+j else s:=s: fi: od: s: end: 0, seq(a(n), n=2..84); # Emeric Deutsch, Feb 24 2006

Mathematica

a[1] = 0; a[n_] := With[{f = FactorInteger[n]}, Select[Range[f[[1, 1]], f[[-1, 1]]], SquareFreeQ] // Total];
Array[a, 100] (* Jean-François Alcover, Aug 24 2020 *)

Crossrefs

Cf. A005117.

Sequence in context: A123528 A374250 A074036 * A074196 A153023 A068319

Adjacent sequences: A074248 A074249 A074250 * A074252 A074253 A074254

Keyword

nonn

Author

Jason Earls, Sep 20 2002

Status

approved