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 A048055 Numbers n such that (sum of the nonprime proper divisors of n) - (sum of prime divisors of n) = n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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) LINKS Donovan Johnson, Table of n, a(n) for n = 1..34 (terms <= 10^12) Donovan Johnson, 82 terms > 10^12 Peter Luschny, Zumkeller Numbers. EXAMPLE 532 = 1 - 2 + 4 - 7 + 14 - 19 + 28 + 38 + 76 + 133 + 266. MAPLE # 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) MATHEMATICA zummableQ[n_] := DivisorSigma[1, n] == 2*(n + Total[Select[Divisors[n], PrimeQ]]); n = 2; A048055 = {}; While[n < 10^6, If[zummableQ[n], Print[n]; AppendTo[A048055, n]]; n++]; A048055 (* Jean-François Alcover, Dec 07 2011, after Peter Luschny *) PROG (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 (Python) from sympy import divisors, primefactors A048055 = [] for n in range(1, 10**4): ....s = sum(divisors(n)) ....if not s % 2 and 2*n <= s and (s-2*n)/2 == sum(primefactors(n)): ........A048055.append(n) # Chai Wah Wu, Aug 20 2014 CROSSREFS Cf. A083207, A105221, A060278, A000203, A027751, A010051, A002808. Sequence in context: A174780 A191950 A333102 * A067803 A098258 A160176 Adjacent sequences:  A048052 A048053 A048054 * A048056 A048057 A048058 KEYWORD nonn,nice AUTHOR EXTENSIONS 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 STATUS approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)