A254879 Let us denote 's' the sum of the deficient numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s)-s is equal to x.

6, 28, 54, 284, 496, 1184, 1210, 2924, 5564, 6232, 6368, 8128, 10744, 10856, 14595, 18150, 18416, 66928, 66992, 71145, 76084, 87633, 88730, 123152, 124155, 139815, 153176, 168730, 176336, 180848, 193720, 202444, 203432, 365084, 389924, 399592, 430402, 455344

Offset: 1

Author

Paolo P. Lava, Feb 10 2015

Keywords

• nonn

Comments

Perfect numbers belong to the sequence.

Examples

			Aliquot parts of 28 are 1, 2, 4, 7, 14 and they are all deficient numbers: sigma(1 + 2 + 4 + 7 + 14) = sigma(28) = 56 and 56 - 28 = 28.
Aliquot parts of 18150 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 121, 150, 165, 242, 275, 330, 363, 550, 605, 726, 825, 1210, 1650, 1815, 3025, 3630, 6050, 9075 and the deficient numbers are 1, 2, 3, 5,10, 11, 15, 22, 25, 33, 50, 55, 75, 110, 121, 165, 242, 275, 363, 605, 825, 1210, 1815, 3025, 9075:  sigma(1 + 2 + 3 + 5 + 10 + 11 + 15 + 22 + 25 + 33 + 50 + 55 + 75 + 110 + 121 + 165 + 242 + 275 + 363 + 605 + 825 + 1210 + 1815 + 3025 + 9075) = 18138 and sigma(18138) - 18138 = 18150.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000396, A001065, A005100, A254878, A254880.

Programs

Maple

with(numtheory); P:=proc(q) local a,b,k,n;
for n from 1 to q do a:=sort([op(divisors(n))]); b:=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)-b=n then print(n); fi; od; end: P(10^9);