A223609 -id:A223609 - cp's OEIS frontend

A109788 Admirable numbers whose abundance is < 10.

12, 20, 56, 70, 88, 104, 368, 464, 650, 836, 1888, 1952, 4030, 5830, 8925, 11096, 17816, 32128, 32445, 45356, 77744, 91388, 128768, 130304, 254012, 388076, 442365, 521728, 522752, 1848964, 2087936, 2291936, 8378368, 8382464, 13174976, 29465852, 35021696, 45335936

Offset: 1

Jason Earls, Aug 14 2005

nonn

Apparently all the abundant numbers with even abundance < 10 are admirable (checked for the first 60 terms). Of the 4 known numbers whose abundance is 10 (A223609), only the first, 40, is admirable. - Amiram Eldar, Nov 07 2019

Amiram Eldar, Table of n, a(n) for n = 1..60

Cf. A033880, A111592, A111667.

aQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab < 10 && ab/2 < n && Divisible[n, ab/2]; Select[Range[10^4], aQ] (* Amiram Eldar, Nov 07 2019 *)

for(n=1,10^9,my(ap=sigma(n)-2*n); if(ap>0 && ap<10 && ap%2==0, my(d=ap/2); if(d!=n && n%d==0, print1(n, ", ")))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

a(36)-a(38) from Amiram Eldar, Nov 07 2019

A063788 Numbers k such that sigma(k) = 2k + Omega(k), where Omega(n) is the number of prime divisors of n (with repetition).

Original entry on oeis.org

18, 88, 4030, 5830, 518656, 13174976, 134094848, 2146926592, 2251798907715584, 12504224434300196, 324257317741920256

Offset: 1

Jason Earls, Aug 16 2001

Includes terms 633825300114085990300727115776 and 2596148429267411760623818083663872. - Donovan Johnson, Dec 19 2008; edited by Max Alekseyev, May 27 2025

Terms a(2)-a(4) come from A088832, a(5) from A223609, a(6) and a(10) from A088833, a(7) from A141546, a(8) from A141547, a(9) from A275701, a(11) from A223611. Also includes the following terms k with Omega(k) = 56: 246434407522188377975875310632234056969345758857269346304, 15937923506379504700185810932457673797717574263217988829184, 264936582814027097239593278653623212574863771975442952634761216, 7948097484419456643668355219907727481405487440330234556835692544. - Max Alekseyev, May 27 2025

Cf. A000203 (sigma), A001222 (Omega), A088832, A223609, A088833, A141546, A141547, A275701, A223611.

for(n=1,10^8, if(sigma(n)==2*n+bigomega(n),print(n)))

Numbers k such that A000203(k) = 2k + A001222(k). - Wesley Ivan Hurt, Oct 30 2022

a(7)-a(8) from Donovan Johnson, Dec 19 2008

a(9) from Donovan Johnson confirmed and a(10)-a(11) added by Max Alekseyev, May 27 2025

cp's OEIS Frontend

A109788 Admirable numbers whose abundance is < 10.

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