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A330786 Number of steps to reach 1 by iterating the absolute alternating sum-of-divisors function (A206369). 3
0, 1, 2, 3, 4, 2, 3, 5, 4, 4, 5, 3, 4, 3, 6, 6, 7, 4, 5, 4, 4, 5, 6, 5, 5, 4, 5, 5, 6, 6, 7, 5, 5, 7, 6, 5, 6, 5, 6, 5, 6, 4, 5, 7, 6, 6, 7, 6, 6, 5, 6, 6, 7, 5, 6, 7, 6, 6, 7, 6, 7, 7, 5, 6, 7, 5, 6, 7, 8, 6, 7, 7, 8, 6, 5, 6, 7, 6, 7, 8, 8, 6, 7, 6, 7, 5, 8, 6, 7, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A preliminary for investigating iterates of A206369.
REFERENCES
See A206369.
LINKS
FORMULA
a(1) = 0; for n > 1, a(n) = 1 + a(A206369(n)).
EXAMPLE
Iterating A206369 with a starting value of 27 gives 20, 12, 6, 2, 1, taking 5 steps to reach 1. So a(27) = 5.
MATHEMATICA
f[p_, e_] := Sum[(-1)^(e-k)*p^k, {k, 0, e}]; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); a[n_] := Length @ FixedPointList[s, n] - 2; Array[a, 90] (* Amiram Eldar, Jan 01 2020 *)
PROG
(PARI) f(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ A206369
a(n) = {if (n==1, return (0)); my(nb = 1); while ((n = f(n)) != 1, nb++); nb; } \\ Michel Marcus, Jan 01 2020
CROSSREFS
Cf. A206369.
Sequence in context: A274640 A245341 A215088 * A182985 A304113 A304112
KEYWORD
nonn
AUTHOR
Allan C. Wechsler, Dec 31 2019
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)