A222087 Numbers n for which A222084(n)= A222084(A222085(n)).

1, 2, 6, 14, 15, 20, 22, 24, 33, 38, 46, 49, 51, 52, 62, 63, 86, 87, 91, 92, 93, 95, 118, 119, 121, 141, 142, 143, 145, 147, 148, 153, 158, 159, 165, 166, 169, 183, 198, 206, 210, 215, 217, 219, 244, 247, 249, 253, 262, 267, 270, 278, 279, 286, 287, 295, 301

Offset: 1

Author

Paolo P. Lava, Feb 13 2013

Keywords

• nonn

Comments

Similar to A037197 but using tau#(n), number of the least divisors of n whose LCM is equal to n, as defined in A222084, and sigma#(n), sum of the least divisors of n whose LCM is equal to n, as defined in A222085: tau#(n)=tau#(sigma#(n)).

If we add also the restriction tau(n)=tau(sigma(n)) we have: 2, 52, 1525, 83667, 116162,…

Examples

			n=20; tau#(20)=4, sigma#(20)=12 and tau#(sigma#(20))=tau#(12)=4.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.

Programs

Maple

with(numtheory);
A222087:=proc(q)
local a,b,c,j,n,t,v;
print(1);
for n from 2 to q do
  a:=ifactors(n)[2]; b:=nops(a); c:=0; v:=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));
  for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od; t:=j;
  a:=ifactors(v)[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(v))])); b:=nops(divisors(v));
  for j from 1 to b do if a[j]=c then break; fi; od; if t=j then print(n);
fi; od; end:
A222087(10000000000);