A138828 - OEIS

%I #25 Feb 07 2019 13:31:08

%S 6,10,19,19,28,64,55,73,190,235,289,352,1405,1711,3520,5833,5968,8821,

%T 11548,11791,26317,27298,30232,53740,58960,62956,120898,233722,299314,

%U 356860,585478,2048248,2329372,3405232,3789352,8056495,8186041,18894079,36485416,56880973,65115946,70334902,82384129

%N Sum of digits of n-th even perfect number.

%H Ivan Panchenko, <a href="/A138828/b138828.txt">Table of n, a(n) for n = 1..47</a>

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%F a(n) = A007953(A000396(n)). - _R. J. Mathar_, May 22 2008 [This assumes that all perfect numbers are even. - _Ivan Panchenko_, Aug 16 2018]

%t 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 *)

%t 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 *)

%Y Cf. A000396, A007605, A066538, A138127.

%K base,nonn

%O 1,1

%A _Omar E. Pol_, Apr 01 2008

%E More terms from _R. J. Mathar_, May 22 2008

%E a(15)-a(38) from _Donovan Johnson_, Nov 09 2010

%E Definition changed (inserting the word "even") and a(39)-a(43) added by _Ivan Panchenko_, Aug 06 2018