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%I #23 Mar 03 2024 10:15:45
%S 11,19,22,37,38,39,41,46,47,51,55,57,58,59,61,62,65,67,68,73,74,76,78,
%T 79,87,88,91,92,99,102,104,107,113,114,115,116,118,123,124,125,127,
%U 129,131,132,133,136,138,139,142,143,146,148,149,153,155,156,157,159
%N Numbers k such that k and k + 5040 have the same number of divisors.
%C Claudia Spiro proved in 1981 that this sequence is infinite. Her work helped D. R. Heath-Brown to prove in 1984 that A005237 is also infinite.
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, p. 111.
%D Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996, p. 332.
%D Joe Roberts, Lure of the Integers, The Mathematical Association of America, 1992, p. 69.
%H Robert Israel, <a href="/A284783/b284783.txt">Table of n, a(n) for n = 1..10000</a>
%H Claudia A. Spiro, <a href="https://www.proquest.com/openview/3c72b874bc57946ce415a828b143fd22/">The Frequency with Which an Integral-Valued, Prime-Independent, Multiplicative or Additive Function of n Divides a Polynomial Function of n</a>, Ph. D. Thesis, University of Illinois, Urbana-Champaign, 1981.
%t Select[Range[160], DivisorSigma[0, #] == DivisorSigma[0, # + 5040] &]
%o (PARI) for(n=1, 200, if(numdiv(n) == numdiv(n + 5040), print1(n,", "))) \\ _Indranil Ghosh_, Apr 04 2017
%o (Python)
%o from sympy.ntheory import divisor_count as D
%o print([n for n in range(1, 201) if D(n) == D(n + 5040)]) # _Indranil Ghosh_, Apr 04 2017
%Y Cf. A000005, A005237.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 02 2017
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