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

Author

Madaline McCluskey, Mar 21 2014

Keywords

• nonn

Examples

			First perfect number is 6, its two prime factors are 2 and 3, so a(1) = 5.
		

Crossrefs

Cf. A000396, A008472.

Programs

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) = A008472(A000396(n)). - Michel Marcus, Mar 21 2014

a(n) = A000668(n) + 2 (conjectured). - Michel Marcus, Mar 21 2014

Extensions

Typo in data corrected by Michel Marcus, Mar 21 2014