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

Author

Paolo P. Lava, Feb 10 2015

Keywords

• nonn
• more

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

Examples

			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.
		

Crossrefs

Cf. A000043, A000203, A005100, A254879, A254880.

Programs

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[10000], seqQ] (* Amiram Eldar, Mar 24 2019 *)

PARI

isok(n) = my (s = sumdiv(n, d, d*((d!=n) && (sigma(d)/d < 2)))); s && (sigma(s) == n); \\ Michel Marcus, Feb 19 2015

Extensions

a(11) from Amiram Eldar, Mar 24 2019