A284783 Numbers k such that k and k + 5040 have the same number of divisors.

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Claudia A. Spiro, The Frequency with Which an Integral-Valued, Prime-Independent, Multiplicative or Additive Function of n Divides a Polynomial Function of n, Ph. D. Thesis, University of Illinois, Urbana-Champaign, 1981.

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

Cf. A000005, A005237.

Sequence in context: A328870 A244287 A065126 * A145059 A124139 A291682

Adjacent sequences: A284780 A284781 A284782 * A284784 A284785 A284786

Keyword

nonn

Author

Amiram Eldar, Apr 02 2017

Status

approved