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 A086793 Number of iterations of the map A034690 (x -> sum of digits of all divisors of x) required to reach one of the fixed points, 15 or 1. 14
 0, 5, 4, 3, 9, 8, 2, 1, 11, 12, 5, 7, 10, 1, 0, 13, 12, 15, 6, 1, 2, 12, 9, 9, 11, 1, 13, 9, 8, 14, 10, 14, 8, 16, 3, 17, 6, 10, 2, 14, 9, 9, 2, 3, 9, 16, 8, 3, 3, 3, 16, 2, 12, 4, 16, 4, 2, 14, 1, 10, 2, 1, 15, 7, 3, 18, 2, 18, 10, 18, 12, 11, 6, 10, 17, 10, 10, 17, 13, 10, 11, 16, 8, 2, 14, 10, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Ecker states that every number (larger than 1) eventually reaches 15. "Take any natural number larger than 1 and write down its divisors, including 1 and the number itself. Now take the sum of the digits of these divisors. Iterate until a number repeats. The black-hole number this time is 15." [Ecker] The only other fixed point of A034690, namely 1, cannot be reached by any other starting value than 1 itself. - M. F. Hasler, Nov 08 2015 REFERENCES Michael W. Ecker, Number play, calculators and card tricks ..., pp. 41-51 of The Mathemagician and the Pied Puzzler, Peters, Boston. [Suggested by a problem in this article.] LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (corrected by Georg Fischer, Jan 20 2019) Eric Angelini et al., List the dividers, sum the digits, SeqFan list, Nov. 2015 Michael W. Ecker, Divisive Number 15. (Web archive, as of May 2008) EXAMPLE 35 requires 3 iterations to reach 15 because 35 -> 1+5+7+3+5 = 21 -> 1+3+7+2+1 = 14 -> 1+2+7+1+4 = 15. MAPLE with(numtheory); read transforms; f:=proc(n) local t1, t2, i; t1:=divisors(n); t2:=0; for i from 1 to nops(t1) do t2:=t2+digsum(t1[i]); od: t2; end; g:=proc(n) global f; local t2, i; t2:=n; for i from 1 to 100 do if t2 = 15 then return(i-1); fi; t2:=f(t2); od; end; # N. J. A. Sloane MATHEMATICA f[n_] := (i++; Plus @@ Flatten@IntegerDigits@Divisors@n); Table[i = 0; NestWhile[f, n, # != 15 &]; i, {n, 2, 87}] (* Robert G. Wilson v, May 16 2006 *) PROG (Haskell) a086793 = f 0 where    f y x = if x == 15 then y else f (y + 1) (a034690 x) -- Reinhard Zumkeller, May 20 2015 (PARI) A086793(n)=n>1&&for(k=0, 9e9, n==15&&return(k); n=A034690(n)) \\ M. F. Hasler, Nov 08 2015 CROSSREFS Cf. A034690, A114527. For records see A095347, A118358. Sequence in context: A202412 A194556 A154198 * A070515 A096733 A125900 Adjacent sequences:  A086790 A086791 A086792 * A086794 A086795 A086796 KEYWORD base,easy,nonn AUTHOR Jason Earls, Aug 04 2003; revised Jun 03 2004 EXTENSIONS Corrected by N. J. A. Sloane, May 17 2006 (a(15) changed to 0) Corrected by David Applegate, Jan 23 2007 (reference book title corrected) Extended to a(1)=0 by M. F. Hasler, Nov 08 2015 STATUS approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)