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A274205 Numbers such that the sum of divisors is twice the sum of the exponential divisors. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A277014 A033581 A213393 * 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

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)