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 A074251 Sum of the squarefree numbers from the smallest prime factor of n to the largest prime factor of n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A318675 A123528 A074036 * A074196 A153023 A068319 Adjacent sequences: A074248 A074249 A074250 * A074252 A074253 A074254 KEYWORD nonn AUTHOR Jason Earls, Sep 20 2002 STATUS approved

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)