A219016 e-perfect numbers (A054979) divided by 36.

1, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 37, 41, 43, 47, 50, 53, 55, 59, 61, 65, 67, 71, 73, 75, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 127, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 161, 163, 167, 173, 179, 181, 185, 187

Offset: 1

Author

Jon Perry, Nov 13 2012

Keywords

• nonn

Comments

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]

Examples

			A054979(3)=252 so a(3)=7.
The e-divisors of 36*50 = 1800 are 30, 120, 90, 360, 150, 600, 450 and 1800, which sum to 3600 as required.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054979.

Programs

Mathematica

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

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