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%I #11 Jan 04 2023 01:30:58
%S 1,2,6,24,30,36,42,192,216,240,264,288,312,336,360,480,510,540,570,
%T 600,630,660,690,720,750,780,810,840,870,900,930,1152,1188,1224,1260,
%U 1296,1332,1368,1404,1440,1476,1512,1548,1584,1620,1656,1692,1728,1764,1800,1836
%N a(1) = 1, a(2) = 2; thereafter a(n) = n * a(A070939(n)).
%C Problem A6 of the 63rd Putnam Competition (2002) asked to prove that when this sequence is generalized to base-b digits, the sum of reciprocals converges only for b = 2.
%C Problem 2 in Appendix D of Bornemann et al. (2004) asked to calculate the sum of the reciprocals of this sequence.
%D Daniel D. Bonar and Michael J. Khoury, Jr., Real infinite Series, The Mathematical Association of America, 2006, pp. 159, 190-191.
%D Hongwei Chen, Classical Analysis: An Approach through Problems, CRC Press, 2022, p. 118, exercise 34.
%D Kiran S. Kedlaya, Daniel M. Kane, Jonathan M. Kane, and Evan M. O'Dorney, The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions, and Commentary, American Mathematical Society, 2020, pp. 86-87.
%H Amiram Eldar, <a href="/A359450/b359450.txt">Table of n, a(n) for n = 1..10000</a>
%H Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/">The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing</a>, SIAM, Philadelphia, 2004. See <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/AppendixD/AppendixD.pdf">Appendix D</a>, Problem 2, p. 281.
%H Kiran Kedlaya and Lenny Ng, <a href="https://kskedlaya.org/putnam-archive/2002s.pdf">Solutions to the 63rd William Lowell Putnam Mathematical Competition</a>, Saturday, December 7, 2002. See Problem A-6, p. 2.
%H Leonard F. Klosinski, Gerald L. Alexanderson, and Loren C. Larson, <a href="https://www.jstor.org/stable/3647854">The Sixty-Third William Lowell Putnam Mathematical Competition</a>, The American Mathematical Monthly, Vol. 110, No. 8 (2003), pp. 718-726.
%H John Scholes, <a href="https://prase.cz/kalva/putnam/psoln/psol026.html">Problem A6</a>, The 63rd Putnam Competition, 2002.
%H David Smith, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/AppendixD/">On a slowly converging sum</a>, Solution to Problem 2, 2003.
%F Sum_{n>=1} 1/a(n) = A359451.
%t a[1] = 1; a[2] = 2; a[n_] := a[n] = n * a[BitLength[n]]; Array[a, 100]
%o (PARI) a(n) = if(n < 3, n, n * a(#binary(n)));
%Y Cf. A070939, A359451.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Jan 02 2023
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