A239546 Sum of the prime factors of n, where n runs through perfect numbers.
5, 9, 33, 129, 8193, 131073, 524289, 2147483649, 2305843009213693953, 618970019642690137449562113, 162259276829213363391578010288129, 170141183460469231731687303715884105729
Offset: 1
Keywords
Examples
First perfect number is 6, its two prime factors are 2 and 3, so a(1) = 5.
Programs
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Mathematica
(* based on the code of Harvey P. Dale in A000396 *) perf=(# (#+1))/2&/@Select[2^Range[1000]-1,PrimeQ]; spf[n_]:=Total[First/@FactorInteger[n]];spf/@perf (* Ivan N. Ianakiev, Jul 11 2015 *)
Formula
a(n) = A000668(n) + 2 (conjectured). - Michel Marcus, Mar 21 2014
Extensions
Typo in data corrected by Michel Marcus, Mar 21 2014