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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
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
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, # &, #<n && DivisorSigma[1, #] < 2# &]}, s>0 && DivisorSigma[1, s] == n]; Select[Range[10000], 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
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Feb 10 2015
EXTENSIONS
a(11) from Amiram Eldar, Mar 24 2019
STATUS
approved