A274205 Numbers such that the sum of divisors is twice the sum of the exponential divisors.

6, 24, 54, 216, 1638, 6552, 14256, 55860, 80262, 276822, 321048, 502740, 1107288, 1396500, 1724976, 12568500, 13564278, 20165460, 54257112, 168836850, 181489140, 504136500, 675347400, 4537228500, 28533427650, 60950102850, 114133710600, 162252212850, 243800411400, 649008851400, 734916514878

Offset

1,1

Comments

All terms appear to be multiples of 6.

Subset of A011775, A069235, A175200, A215142.

a(32) > 10^12. If p*r is a term, where p is prime and r is not divisible by p, then p^3*r is also a term. - Giovanni Resta, Jun 15 2016

Links

Table of n, a(n) for n=1..31.

Example

Divisors of 6 are 1, 2, 3 and 6 which sum to 12. The only exponential divisor is 6. Finally 12 / 6 = 2.
Divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 which sum to 60. Exponential divisors are 6, 24 and their sum is 30. Finally 60 / 30 = 2.

Maple

with(numtheory): P:=proc(q) local a, b, c, d, j, k, n, ok;
for n from 2 to q do a:=ifactors(n)[2]; b:=sort([op(divisors(n))]); c:=0;
for k from 2 to nops(b) do d:=ifactors(b[k])[2]; if nops(d)=nops(a) then
ok:=1; for j from 1 to nops(d) do if not type(a[j][2]/d[j][2], integer) then ok:=0; break; fi; od;
if ok=1 then c:=c+b[k]; fi;  fi; od; if sigma(n)=2*c  then print(n); fi; od; end: P(10^9);

Mathematica

Select[Range[10^6], 2 Times @@ Map[Sum[First[#]^d, {d, Divisors@ Last@ #}] &, FactorInteger@ #] == DivisorSigma[1, #] &] (* Michael De Vlieger, Jun 16 2016 *)

Crossrefs

Cf. A000203, A011775, A051377, A069235, A175200, A215142.

Sequence in context: A033581 A213393 A334701 * A009943 A028595 A002653

Adjacent sequences: A274202 A274203 A274204 * A274206 A274207 A274208

Keyword

nonn

Author

Paolo P. Lava, Jun 13 2016

Extensions

a(16)-a(31) from Giovanni Resta, Jun 15 2016

Status

approved