A138828 Sum of digits of n-th even perfect number.
6, 10, 19, 19, 28, 64, 55, 73, 190, 235, 289, 352, 1405, 1711, 3520, 5833, 5968, 8821, 11548, 11791, 26317, 27298, 30232, 53740, 58960, 62956, 120898, 233722, 299314, 356860, 585478, 2048248, 2329372, 3405232, 3789352, 8056495, 8186041, 18894079, 36485416, 56880973, 65115946, 70334902, 82384129
Offset: 1
Links
- Ivan Panchenko, Table of n, a(n) for n = 1..47
- Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Programs
-
Mathematica
a[n_] := Block[{e, p, mpe = MersennePrimeExponent@n}, Plus @@ IntegerDigits[(2^mpe - 1) 2^(mpe - 1)]]; Array[a, 44] (* Robert G. Wilson v, Aug 06 2018 *) Total[IntegerDigits[#]]&/@Table[PerfectNumber[n],{n,43}] (* Requires Mathematica version 10 or later *) (* The program may take a long time to run *) (* Harvey P. Dale, Feb 07 2019 *)
Formula
a(n) = A007953(A000396(n)). - R. J. Mathar, May 22 2008 [This assumes that all perfect numbers are even. - Ivan Panchenko, Aug 16 2018]
Extensions
More terms from R. J. Mathar, May 22 2008
a(15)-a(38) from Donovan Johnson, Nov 09 2010
Definition changed (inserting the word "even") and a(39)-a(43) added by Ivan Panchenko, Aug 06 2018