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

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

Offset: 1

Author

Jason Earls, Aug 16 2001

Keywords

• more
• nonn

Comments

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

Crossrefs

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

Programs

PARI

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

Formula

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

Extensions

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