A222085 Sum of the least divisors of n whose LCM is equal to n.

1, 3, 4, 7, 6, 6, 8, 15, 13, 8, 12, 10, 14, 10, 9, 31, 18, 21, 20, 12, 11, 14, 24, 24, 31, 16, 40, 14, 30, 11, 32, 63, 15, 20, 13, 25, 38, 22, 17, 20, 42, 19, 44, 18, 18, 26, 48, 52, 57, 43, 21, 20, 54, 66, 17, 22, 23, 32, 60, 15, 62, 34, 20, 127, 19, 23, 68

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava)

Example

The divisors of 20 are 1, 2, 4, 5, 10, 20 while the least divisors of 20 whose LCM is equal to 20 are 1, 2, 4, 5. Then a(20) = 1+2+4+5 = 12.

Maple

with(numtheory);
A222085:=proc(q)
local a, b, c, j, n, v; print(1);
for n from 2 to q do a:=ifactors(n)[2]; b:=nops(a); c:=0;
  for j from 1 to b do if a[j][1]^a[j][2]>c then c:=a[j][1]^a[j][2]; fi; od;
  a:=op(sort([op(divisors(n))])); b:=nops(divisors(n)); v:=0;
  for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od; print(v);
od; end:
A222085(100000000);

Mathematica

s[n_] := Module[{sum=0, L=1}, Do[sum+=d; L = LCM[L, d]; If[L == n, Break[]], {d, Divisors[n]}]; sum]; Array[s, 67] (* Amiram Eldar, Nov 05 2019 *)

Prog

(PARI) a(n)=my(s, L=1); fordiv(n, d, s+=d; L=lcm(L, d); if(L==n, return(s))) \\ Charles R Greathouse IV, Feb 14 2013

Crossrefs

Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084.

Sequence in context: A230289 A367502 A023888 * A187793 A284326 A117553

Adjacent sequences: A222082 A222083 A222084 * A222086 A222087 A222088

Keyword

nonn

Author

Paolo P. Lava, Feb 11 2013

Status

approved