

A058971


For a rational number p/q let f(p/q) = sum of divisors of p+q divided by number of divisors of p+q; a(n) is obtained by iterating f, starting at n/1, until an integer is reached, or if no integer is ever reached then a(n) = 0.


8



3, 2, 6, 3, 3, 4, 10, 87, 6, 6, 9, 7, 6, 6, 87, 9, 6, 10, 7, 8, 9, 12, 9, 15, 12, 10, 16, 15, 9, 16, 12, 12, 15, 12, 87, 19, 15, 14, 19, 21, 12, 22, 14, 13, 18, 24, 34, 19, 12, 18, 0, 27, 15, 18, 15, 20, 24, 30, 14, 31, 24, 18, 51, 21, 18, 34, 21, 24, 18, 36, 24, 37, 30, 21, 37
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OFFSET

1,1


COMMENTS

a(p1) = (p+1)/2 for all odd primes p. Thus there are infinitely many distinct terms.  Ely Golden, Mar 03 2018


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
P. Schogt, The Wild Number Problem: math or fiction?, arXiv preprint arXiv:1211.6583 [math.HO], 2012.  From N. J. A. Sloane, Jan 03 2013


EXAMPLE

1 > (1+2)/2 = 3/2 > (1+5)/2 = 3, so a(1) = 3. 51 > 49/3 > 49/3 > ..., so a(51) = 0.


MAPLE

with(numtheory); f := proc(n) if whattype(n) = integer then sigma(n+1)/sigma[0](n+1) else sigma(numer(n)+denom(n))/sigma[0](numer(n)+denom(n)); fi; end;


MATHEMATICA

f[x_] := With[{p = Numerator[x], q = Denominator[x]}, DivisorSigma[1, p+q]/DivisorSigma[0, p+q]]; a[n_] := If[ IntegerQ[ r = FixedPoint[f, n, SameTest > (#1 == #2  IntegerQ[#2] &)]], r, 0]; Table[a[n], {n, 1, 75}] (* JeanFrançois Alcover, Jul 18 2012 *)


PROG

(Haskell)
import Data.Ratio ((%), numerator, denominator)
a058971 n = f [n % 1] where
f xs@(x:_)  denominator y == 1 = numerator y
 y `elem` xs = 0
 otherwise = f (y : xs)
where y = (a000203 x') % (a000005 x')
x' = numerator x + denominator x
 Reinhard Zumkeller, Aug 02 2012


CROSSREFS

Cf. A058972, A058977.
Sequence in context: A263353 A248945 A131969 * A186204 A137324 A011209
Adjacent sequences: A058968 A058969 A058970 * A058972 A058973 A058974


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane, Jan 14 2001


EXTENSIONS

More terms from Matthew Conroy, Apr 18 2001, who remarks that a(51) = a(655) = a(1039) = 0 are all the zeros of a(n) for n<10^5.
No more zero terms <= 10^6 found by Reinhard Zumkeller, Aug 02 2012


STATUS

approved



