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.

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

Links

Table of n, a(n) for n=1..11.

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

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