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A048055
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Numbers n such that (sum of the nonprime proper divisors of n) - (sum of prime divisors of n) = n.
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2
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532, 945, 2624, 5704, 6536, 229648, 497696, 652970, 685088, 997408, 1481504, 11177984, 32869504, 52813084, 132612224, 224841856, 2140668416, 2404135424, 2550700288, 6469054976, 9367192064, 19266023936, 23414463358, 31381324288, 45812547584, 55620289024
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OFFSET
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1,1
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COMMENTS
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Contribution from Peter Luschny, Dec 14 2009: (Start)
A member of this sequence is a Zumkeller number [A083207] since the set of its divisors can be partitioned into two disjoint parts so that the sums of the two parts are equal.
1 + sigma*(n) = sigma'(n) + n
sigma*(n) := sum{1<d<n, d|n, d not prime}, [A060278],
sigma'(n) := sum{1<d<n, d|n, d prime}, [A105221]. (End)
138067560448, 142359382016, 181589313536, 227458156544, 239528904704, 325030037504, 432057337856, 670856972288, 7872265324544, 9596286476288, 23479139158016, 518851783499776, 562922036166656, 1021191247659008, 1363337772285952, 72073527964008448, 113444902715654144 and 302019159275995136 are also in the sequence (not necessarily the next 18 terms). - Donovan Johnson, Feb 09 2012
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LINKS
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Table of n, a(n) for n=1..26.
Peter Luschny, Zumkeller Numbers. [From Peter Luschny, Dec 14 2009]
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EXAMPLE
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E.g. 532=1-2+4-7+14-19+28+38+76+133+266.
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MAPLE
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Contribution from Peter Luschny, Dec 14 2009: (Start)
with(numtheory): A048055 := proc(n) local k;
if sigma(n)=2*(n+add(k, k=select(isprime, divisors(n))))
then n else NULL fi end: seq(A048055(i), i=1..7000); (End)
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MATHEMATICA
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ok[n_] := DivisorSigma[1, n] == 2*(n + Total[ Select[ Divisors[n], PrimeQ]]); n = 2; A048055 = {}; While[n < 10^6, If[ok[n], Print[n]; AppendTo[ A048055, n]]; n++]; A048055 (* From Jean-François Alcover, Dec 07 2011, after Peter Luschny *)
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PROG
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(Haskell)
import Data.List (partition)
a048055 n = a048055_list !! (n-1)
a048055_list = [x | x <- a002808_list,
let (us, vs) = partition ((== 1) . a010051) $ a027751_row x,
sum us + x == sum vs]
-- Reinhard Zumkeller, Apr 05 2013
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CROSSREFS
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Cf. A083207, A105221, A060278, A000203 [From Peter Luschny, Dec 14 2009]
Cf. A027751, A010051, A002808.
Sequence in context: A098257 A174780 A191950 * A067803 A098258 A160176
Adjacent sequences: A048052 A048053 A048054 * A048056 A048057 A048058
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KEYWORD
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nonn,nice
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AUTHOR
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Naohiro Nomoto
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EXTENSIONS
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a(15)-a(19) from Donovan Johnson, Dec 07 2008
a(20)-a(24) from Donovan Johnson, Jul 06 2010
a(25)-a(26) from Donovan Johnson, Feb 09 2012
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STATUS
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approved
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