A058974 a(n) = 0 if n = 1 or a prime, otherwise a(n) = s + a(s) iterated until no change occurs, where s (A008472) is sum of distinct primes dividing n.
0, 0, 0, 2, 0, 5, 0, 2, 3, 7, 0, 5, 0, 12, 10, 2, 0, 5, 0, 7, 17, 13, 0, 5, 5, 25, 3, 12, 0, 17, 0, 2, 26, 19, 17, 5, 0, 38, 18, 7, 0, 17, 0, 13, 10, 30, 0, 5, 7, 7, 27, 25, 0, 5, 18, 12, 35, 31, 0, 17, 0, 59, 17, 2, 23, 18, 0, 19, 51, 26, 0, 5, 0, 57, 10, 38, 23, 23, 0, 7, 3, 43, 0, 17, 35, 55, 34, 13, 0
Offset: 1
Keywords
References
- E. N. Gilbert, An interesting property of 38, unpublished, circa 1992. Shows that 38 is the only solution of a(n) = n.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
-
Maple
f := proc(n) option remember; local i,j,k,t1,t2; if n = 1 or isprime(n) then 0 else A008472(n) + f(A008472(n)); fi; end;
-
Mathematica
f[n_Integer] := If[n == 1 || PrimeQ[n], 0, Plus @@ First[ Transpose[ FactorInteger[n]]]]; Table[Plus @@ Drop[ FixedPointList[f, n], 1], {n, 1, 80}] -
PARI
A008472(n) = vecsum(factor(n)[, 1]); \\ This function from M. F. Hasler, Jul 18 2015 A058974(n) = if((1==n)||isprime(n),0,A008472(n)+A058974(A008472(n))); \\ Antti Karttunen, Oct 30 2017, after the Maple-program.
Extensions
More terms from Antti Karttunen, Oct 30 2017