A088820 Numbers k with abundance radius of 8, i.e., abs(sigma(k)-2*k) = 8.

22, 56, 130, 184, 368, 836, 1012, 2272, 11096, 17816, 18904, 33664, 45356, 70564, 77744, 85936, 91388, 100804, 128768, 254012, 388076, 391612, 527872, 1090912, 2087936, 2291936, 13174976, 17619844, 29465852, 35021696, 45335936, 120888092, 260378492, 381236216

Offset

1,1

Comments

Original definition: Abundance-radius=8, that is Abs[sigma[n]-2n]=8 (either +8 or -8). A045770 from 3rd term complemented by -8 cases.

Links

Amiram Eldar, Table of n, a(n) for n = 1..66 (terms below 10^18, from the b-files at A088833 and A125247)

Example

22 is in the sequence since sigma(22) = 1 + 2 + 11 + 22 = 36 = 2*22 - 8.
56 is in the sequence since sigma(56) = 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120 = 2*56 + 8. - Michael B. Porter, Jul 20 2016

Mathematica

Select[Range[1, 10^6], Abs[DivisorSigma[1, #] - 2 #] == 8 &] (* Vincenzo Librandi, Jul 20 2016 *)

Prog

(PARI) is(n)=abs(sigma(n)-2*n)==8 \\ Use, e.g., select(is, [1..10^5]*2). - M. F. Hasler, Jul 19 2016
(Magma) [n: n in [1..2*10^7] | Abs(DivisorSigma(1, n) - 2*n) eq 8]; // Vincenzo Librandi, Jul 20 2016

Crossrefs

Disjoint union of A088833 (abundance 8) and A125247 (deficiency 8).

Cf. A045770, A045768, A055708, A077374, A088007, A088008, A088010, A088011, A088012, A088818, A088819.

Cf. A000203 (sigma), A033880 (abundance), A005100 (deficient numbers).

Sequence in context: A303582 A289015 A063302 * A058097 A131878 A019506

Adjacent sequences: A088817 A088818 A088819 * A088821 A088822 A088823

Keyword

nonn,changed

Author

Labos Elemer, Oct 20 2003

Extensions

More terms from David Wasserman, Aug 18 2005

Edited by M. F. Hasler, Jul 19 2016

a(33)-a(34) from Amiram Eldar, Mar 11 2025

Status

approved