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

1,4

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E. N. Gilbert, An interesting property of 38, unpublished, circa 1992.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

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}]

Prog

(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.

Crossrefs

Cf. A008472, A061376.

Sequence in context: A105221 A215339 A061376 * A369744 A326059 A019962

Adjacent sequences: A058971 A058972 A058973 * A058975 A058976 A058977

Keyword

nonn

Author

N. J. A. Sloane, Jan 15 2001

Extensions

More terms from Antti Karttunen, Oct 30 2017

Status

approved