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A260964
Numbers n such that sigma(n) = (sigma(n)-n)', where sigma(n) is the sum of the divisors of n and (sigma(n)-n)' is the arithmetic derivative of the sum of aliquot parts of n.
0
24, 492, 2528, 3800, 18416, 526688, 531968, 1084592, 27446468, 1350066372, 2493705728, 7768292812, 15595308928
OFFSET
1,1
COMMENTS
a(14) > 10^11. - Hiroaki Yamanouchi, Sep 11 2015
EXAMPLE
sigma(24) - 24 = 36 and 36' = 60 = sigma(24);
sigma(492) - 492 = 684 and 684' = 1176 = sigma(492).
MAPLE
with(numtheory): P:=proc(q) local a, b, c, p, n; for n from 1 to q do
a:=(sigma(n)-n)*add(op(2, p)/op(1, p), p=ifactors((sigma(n)-n))[2]);
if a=sigma(n) then print(n); fi; od; end: P(10^9);
MATHEMATICA
d[0]=d[1]=0; d[n_] := Total[n / Divide@@@ FactorInteger@ n]; Select[Range[10^5], (s = DivisorSigma[1, #]; s == d[s - #]) &] (* Giovanni Resta, Aug 21 2015 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Aug 18 2015
EXTENSIONS
a(9) from Giovanni Resta, Aug 21 2015
a(10)-a(13) from Hiroaki Yamanouchi, Sep 11 2015
STATUS
approved