|
%I #29 Nov 05 2019 06:52:48
%S 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,
%T 40,14,30,11,32,63,15,20,13,25,38,22,17,20,42,19,44,18,18,26,48,52,57,
%U 43,21,20,54,66,17,22,23,32,60,15,62,34,20,127,19,23,68
%N Sum of the least divisors of n whose LCM is equal to n.
%H Amiram Eldar, <a href="/A222085/b222085.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paolo P. Lava)
%e 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.
%p with(numtheory);
%p A222085:=proc(q)
%p local a,b,c,j,n,v; print(1);
%p for n from 2 to q do a:=ifactors(n)[2]; b:=nops(a); c:=0;
%p 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;
%p a:=op(sort([op(divisors(n))])); b:=nops(divisors(n)); v:=0;
%p for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od; print(v);
%p od; end:
%p A222085(100000000);
%t 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 *)
%o (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
%Y Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084.
%K nonn
%O 1,2
%A _Paolo P. Lava_, Feb 11 2013
|
