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%I #60 Jan 28 2020 22:31:05
%S 1,10,40,81,100,400,640,736,810,1000,1300,1458,1729,1944,2268,2430,
%T 3640,4000,6400,7360,7744,8100,10000,12070,12100,13000,14580,16120,
%U 17290,19440,22680,23632,24300,27010,30250,31003,36400,38152,40000,42282,51142,63504
%N Numbers k with the property that there exists a positive integer multiplier M such that M times the sum of the digits of k, multiplied further by the reversal of this product, gives k.
%C These numbers are related to the taxicab number 1729, which has multiplier 1. This is why they might be called "multiplicative Hardy-Ramanujan numbers".
%C If a(n) is in the sequence, then 10 * a(n) is also in the sequence, with the multiplier 10 times larger. We could call primitive the terms not of this form. Primitive terms which end in 0 are 40, 640, 1300, 2430, 3640, 12070, 12100, 16120, 27010, ... - _M. F. Hasler_, May 27 2018
%H Viorel Nitica, <a href="https://arxiv.org/abs/1805.10739">About some relatives of the taxicab numbers</a>, arXiv:1805.10739 [math.NT], 2018; J. of Int. Seq., 21 (2018), Article 18.9.4. [Where these numbers are introduced.]
%H Viorel Nitica, Andrei Török, <a href="https://arxiv.org/abs/1908.00713">About Some Relatives of Palindromes</a>, arXiv:1908.00713 [math.NT], 2019.
%H Viorel Niţică, Jeroz Makhania, <a href="https://doi.org/10.3390/sym11111374">About the Orbit Structure of Sequences of Maps of Integers</a>, Symmetry (2019), Vol. 11, No. 11, 1374.
%e For k = 1729 the sum of the digits is 19 and M = 1: 19 * 91 = 1729.
%e For k = 122512 the sum of the digits is 13 and M = 31: 13 * 31 = 403 and 403 * 304 = 122512.
%o (PARI) select( is(n,s=sumdigits(n))=n&&!frac(n/=s)&&fordiv(n,M,fromdigits(Vecrev(digits(s*M)))*M==n&&return(1)), [0..10^5]) \\ _M. F. Hasler_, May 27 2018
%Y Subsequence of A005349 (Niven numbers).
%Y Cf. A004086, A011541, A061205, A305130.
%K nonn,base
%O 1,2
%A _Viorel Nitica_, May 26 2018
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