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 A254878 Let 's' denote the sum of the deficient numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s) is equal to x. 2
 4, 8, 32, 128, 168, 224, 756, 8192, 131072, 524288, 2147483648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All numbers of the form 2^A000043(n) belong to the sequence. Terms that are not of this form begin: 168, 224, 756, ... - Amiram Eldar, Mar 24 2019 LINKS EXAMPLE Aliquot parts of 8 are 1, 2, 4 that are all deficient numbers: sigma(1 + 2 + 4) = sigma(7) = 8. Aliquot parts of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and the deficient numbers are 1, 2, 3, 4, 7, 8, 14, 21:  sigma(1 + 2 + 3 + 4 + 7 + 8 + 14 + 21) = sigma(60) = 168. MAPLE with(numtheory); P:=proc(q) local a, b, c, k, n; for n from 1 to q do a:=sort([op(divisors(n))]); b:=0; c:=0; for k from 1 to nops(a)-1 do if sigma(a[k])<2*a[k] then b:=b+a[k]; fi; od; if sigma(b)=n then print(n); fi; od; end: P(10^9); MATHEMATICA seqQ[n_] := Module[{s = DivisorSum[n, # &, #0 && DivisorSigma[1, s] == n]; Select[Range, seqQ] (* Amiram Eldar, Mar 24 2019 *) PROG (PARI) isok(n) = my (s = sumdiv(n, d, d*((d!=n) && (sigma(d)/d < 2)))); s && (sigma(s) == n); \\ Michel Marcus, Feb 19 2015 CROSSREFS Cf. A000043, A000203, A005100, A254879, A254880. Sequence in context: A304940 A068205 A241684 * A247473 A113479 A252540 Adjacent sequences:  A254875 A254876 A254877 * A254879 A254880 A254881 KEYWORD nonn,more AUTHOR Paolo P. Lava, Feb 10 2015 EXTENSIONS a(11) from Amiram Eldar, Mar 24 2019 STATUS approved

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Last modified February 27 19:23 EST 2020. Contains 332308 sequences. (Running on oeis4.)