

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
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OFFSET

1,1


COMMENTS

Claudia Spiro proved in 1981 that this sequence is infinite. Her work helped D. R. HeathBrown 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.
Claudia Spiro, The Frequency with Which an IntegralValued, PrimeIndependent, Multiplicative or Additive Function of n Divides a Polynomial Function of n, Ph.D. Dissertation, University of Illinois at Urbana/Champaign, 1981.


LINKS

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


MAPLE

with(numtheory): P:=proc(q) if nops(divisors(q))=nops(divisors(q+5040)) then q; fi; end: seq(P(k), k=1..10^3); # Paolo P. Lava, Apr 04 2017


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



