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

1,1

Comments

Perfect numbers belong to the sequence.

Links

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

Example

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.

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);

Crossrefs

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

Sequence in context: A120624 A138873 A091307 * A298168 A317478 A353901

Adjacent sequences: A254876 A254877 A254878 * A254880 A254881 A254882

Keyword

nonn

Author

Paolo P. Lava, Feb 10 2015

Status

approved