A088826 Solutions to sigma(n)-2*n = phi(n): abundance of n equals Euler-phi of n.

12, 42, 1242, 6137440, 1385119360, 1588268480

Offset: 1

Author

Labos Elemer, Oct 27 2003

Keywords

• more
• nonn

Comments

a(7) > 10^12. - Donovan Johnson, Feb 29 2012

10^13 < a(7) <= 479535318548480. Other terms of the form 2^k*5*p*q are 983990190817280, 528322308638228480, 1374972658786140160, 9222951307429806080 and 13732480001814200320. - Giovanni Resta, Jul 12 2013

248248256622696037089280 and 29053620223944172891013120 are the next two terms of the form 2^k*5*p*q where p&q are distinct primes. 12, 42 and 1242 are the only terms of one of the three forms 4*p, 2*p*q and 2*p^3*q where p and q are two distinct primes. Farideh Firoozbakht, Aug 19 2013

Examples

			n=1242, sigma(1242)=2880, 2880-2484=396=phi(1242).
		

Crossrefs

Cf. A000203, A000010, A077374, A033880.

Programs

Mathematica

Do[If[Equal[DivisorSigma[1, n]-2*n, EulerPhi[n]], Print[n]], {n, 1, 10000000}]

Extensions

a(5)-a(6) from Donovan Johnson, Sep 30 2009