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

1,2

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]

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A054979.

Sequence in context: A288155 A135775 A353686 * A348753 A276378 A243292

Adjacent sequences: A219013 A219014 A219015 * A219017 A219018 A219019

Keyword

nonn

Author

Jon Perry, Nov 13 2012

Status

approved