OFFSET
1,1
COMMENTS
a(n) and square root of phi(a(n))*sigma(a(n)) + 2*a(n) + 2 are close to each other: e.g., a(7) = 2107519 and this square root is 2107458.
Since (p+1)*(p-1) + 2*(p+1) = p*p + 2*p + 1 = (p+1)^2 is a square, all primes are solutions.
73362272287 and 181264312447 are also terms. - Donovan Johnson, Jul 13 2012
EXAMPLE
k = 7777: sigma(7777) = 9792, phi(7777) = 6000 and 9792*6000 + 2*7778 = 587675556 = 7666^2.
PROG
(PARI) { n=0; for (m=1, 10^12, if (isprime(m), next); s=sigma(m)*eulerphi(m) + 2*(m + 1); if (issquare(s), write("b065656.txt", n++, " ", m); if (n==100, return)) ) } \\ Harry J. Smith, Oct 26 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 12 2001
EXTENSIONS
a(9)-a(15) from Harry J. Smith, Oct 26 2009
a(16)-a(20) from Donovan Johnson, May 24 2011
a(21)-a(25) from Donovan Johnson, Jul 13 2012
STATUS
approved