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A219016 e-perfect numbers (A054979) divided by 36. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 20 08:00 EDT 2022. Contains 353852 sequences. (Running on oeis4.)