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A305131 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. 1
1, 10, 40, 81, 100, 400, 640, 736, 810, 1000, 1300, 1458, 1729, 1944, 2268, 2430, 3640, 4000, 6400, 7360, 7744, 8100, 10000, 12070, 12100, 13000, 14580, 16120, 17290, 19440, 22680, 23632, 24300, 27010, 30250, 31003, 36400, 38152, 40000, 42282, 51142, 63504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These numbers are related to the taxicab number 1729, which has multiplier 1. This is why they might be called "multiplicative Hardy-Ramanujan numbers".

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

LINKS

Table of n, a(n) for n=1..42.

Viorel Nitica, About some relatives of the taxicab numbers, arXiv:1805.10739 [math.NT], 2018; J. of Int. Seq., 21 (2018), Article 18.9.4. [Where these numbers are introduced.]

Viorel Nitica, Andrei Török, About Some Relatives of Palindromes, arXiv:1908.00713 [math.NT], 2019.

Viorel Niţică, Jeroz Makhania, About the Orbit Structure of Sequences of Maps of Integers, Symmetry (2019), Vol. 11, No. 11, 1374.

EXAMPLE

For k = 1729 the sum of the digits is 19 and M = 1: 19 * 91 = 1729.

For k = 122512 the sum of the digits is 13 and M = 31: 13 * 31 = 403 and 403 * 304 = 122512.

PROG

(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

CROSSREFS

Subsequence of A005349 (Niven numbers).

Cf. A004086, A011541, A061205, A305130.

Sequence in context: A000132 A328093 A306830 * A217073 A210376 A060317

Adjacent sequences:  A305128 A305129 A305130 * A305132 A305133 A305134

KEYWORD

nonn,base

AUTHOR

Viorel Nitica, May 26 2018

STATUS

approved

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Last modified May 27 03:03 EDT 2020. Contains 334647 sequences. (Running on oeis4.)