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A212128 Nonprimes whose arithmetic derivative equals the sum of its proper divisors. 3
1, 12, 18, 220, 396, 287532 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(7) > 10^12. - Giovanni Resta, Mar 11 2014

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

The arithmetic derivative of 12 is equal to 16 (see A003415). On the other hand the sum of proper divisors of 12 is equal to 16 since 1+2+3+4+6 = 16, so 12 is in the sequence.

MAPLE

with(numtheory);

A212128:=proc(i) local n, p;

for n from 1 to i do

  if sigma(n)/n-1=add(op(2, p)/op(1, p), p=ifactors(n)[2]) and not isprime(n) then print(n);

fi; od; end:

A212128(10^6); # Paolo P. Lava, Jan 04 2012

MATHEMATICA

dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; Select[Range[300000], ! PrimeQ[#] && dn[#] == DivisorSigma[1, #] - # &] (* T. D. Noe, Dec 27 2012 *)

CROSSREFS

Cf. A018252, A000203, A001065, A003415, A211991, A212127.

Sequence in context: A166627 A018957 A238922 * A110932 A112880 A211083

Adjacent sequences:  A212125 A212126 A212127 * A212129 A212130 A212131

KEYWORD

nonn,more

AUTHOR

Omar E. Pol, Dec 19 2012

STATUS

approved

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Last modified October 21 09:42 EDT 2021. Contains 348150 sequences. (Running on oeis4.)