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

Author

Paolo P. Lava, Feb 11 2013

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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