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A284783
Numbers k such that k and k + 5040 have the same number of divisors.
1
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
OFFSET
1,1
COMMENTS
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.
REFERENCES
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.
MATHEMATICA
Select[Range[160], DivisorSigma[0, #] == DivisorSigma[0, # + 5040] &]
PROG
(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
CROSSREFS
Sequence in context: A328870 A244287 A065126 * A145059 A124139 A291682
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 02 2017
STATUS
approved