A219016 - OEIS

%I #31 Dec 02 2020 18:03:53

%S 1,5,7,11,13,17,19,23,29,31,35,37,41,43,47,50,53,55,59,61,65,67,71,73,

%T 75,77,79,83,85,89,91,95,97,101,103,107,109,113,115,119,127,131,133,

%U 137,139,143,145,149,151,155,157,161,163,167,173,179,181,185,187

%N e-perfect numbers (A054979) divided by 36.

%C All primes except 2 and 3, and squarefree odd numbers, are in this sequence. [It appears that the author may have meant squarefree numbers coprime to 6, not squarefree odd numbers. - _Peter Munn_, Nov 22 2020]

%H Charles R Greathouse IV, <a href="/A219016/b219016.txt">Table of n, a(n) for n = 1..10000</a>

%e A054979(3)=252 so a(3)=7.

%e The e-divisors of 36*50 = 1800 are 30, 120, 90, 360, 150, 600, 450 and 1800, which sum to 3600 as required.

%t ee[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; Select[Range[10000], ee[#] == 2 # &]/36 (* _T. D. Noe_, Nov 14 2012 *)

%o (PARI) is(n)=my(f=factor(36*n)); prod(i=1, #f~, sumdiv(f[i, 2], d, f[i, 1]^d))==72*n \\ _Charles R Greathouse IV_, Dec 30 2013

%Y Cf. A054979.

%K nonn

%O 1,2

%A _Jon Perry_, Nov 13 2012