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A284783
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Numbers k such that k and k + 5040 have the same number of divisors.
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1
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11, 19, 22, 37, 38, 39, 41, 46, 47, 51, 55, 57, 58, 59, 61, 62, 65, 67, 68, 73, 74, 76, 78, 79, 87, 88, 91, 92, 99, 102, 104, 107, 113, 114, 115, 116, 118, 123, 124, 125, 127, 129, 131, 132, 133, 136, 138, 139, 142, 143, 146, 148, 149, 153, 155, 156, 157, 159
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, p. 111.
Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996, p. 332.
Joe Roberts, Lure of the Integers, The Mathematical Association of America, 1992, p. 69.
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LINKS
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MATHEMATICA
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Select[Range[160], DivisorSigma[0, #] == DivisorSigma[0, # + 5040] &]
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PROG
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(PARI) for(n=1, 200, if(numdiv(n) == numdiv(n + 5040), print1(n, ", "))) \\ Indranil Ghosh, Apr 04 2017
(Python)
from sympy.ntheory import divisor_count as D
print([n for n in range(1, 201) if D(n) == D(n + 5040)]) # Indranil Ghosh, Apr 04 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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