A068420 Numbers n such that sigma(n) = 4*(n-phi(n)).

3, 99, 168, 780, 1836, 2976, 5928, 6201, 6468, 13888, 48768, 75696, 123216, 227584, 285948, 401952, 437664, 1003000, 2058732, 3302592, 3810624, 4031488, 4258496, 4318656, 6713664, 14188992, 32021613, 93298284, 201302016, 226196736, 381144320, 514882128

Offset

1,1

Comments

If 2^p-1 is a prime (a Mersenne prime) greater than 3 then 3*2^p*(2^p-1) is in the sequence (the proof is easy). The sequence A110075 gives such terms of this sequence. - Farideh Firoozbakht, Jul 27 2005

If 2^p-1 is a prime (a Mersenne prime) not equal to 7 then 7*2^(p+1)*(2^p-1) is in the sequence (the proof is easy). - Farideh Firoozbakht, Aug 18 2013

Theorem: If 2^p-1 and 2^q-1 are two distinct Mersenne primes then 2^(p+q-2)*(2^p-1)*(2^q-1) is in the sequence (the proof is easy). The two preceding remarks are the special cases q = 2 and q = 3. - Farideh Firoozbakht, Dec 21 2014

Links

Table of n, a(n) for n=1..32.

Mathematica

a068420[n_] := Select[Range[n], DivisorSigma[1, #] == 4 (# - EulerPhi[#]) &]; a068420[10^6] (* Michael De Vlieger, Dec 21 2014 *)

Prog

(PARI) for(n=1, 100000000, if(sigma(n)==4*(n-eulerphi(n)), print1(n, ", ")))

Crossrefs

Cf. A000668, A110075.

Sequence in context: A057014 A334723 A167582 * A276188 A180350 A293952

Adjacent sequences: A068417 A068418 A068419 * A068421 A068422 A068423

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 02 2002

Extensions

More terms from Rick L. Shepherd, Apr 03 2002

a(29)-a(32) from Donovan Johnson, Jun 30 2012

Status

approved