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A152216 For two consecutive numbers, the sum of the divisors of the sum of the two numbers divides the sum of the divisors of the product of the numbers. That is, numbers n such that sigma(2n+1) divides sigma(n^2 + n). 1
2, 5, 7, 11, 19, 20, 23, 28, 29, 32, 34, 38, 39, 41, 46, 53, 57, 59, 62, 70, 73, 77, 83, 89, 90, 94, 103, 104, 113, 118, 119, 124, 131, 160, 173, 177, 179, 188, 190, 191, 208, 227, 229, 233, 239, 242, 248, 251, 263, 280, 281, 290, 293, 297, 298, 311, 316, 327, 335 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
For n=11, 11+12 = 23, sigma(23) = 24; sigma(11*12) = sigma(132) = 336 and 24|336.
MAPLE
for n from 1 to 500 do if numtheory[sigma](n*(n+1)) mod numtheory[sigma](2*n+1) = 0 then printf("%d, ", n); fi; od: # R. J. Mathar, Dec 04 2008
with(numtheory): a := proc (n) if type(sigma(n^2+n)/sigma(2*n+1), integer) = true then n else end if end proc: seq(a(n), n = 1 .. 400); # Emeric Deutsch, Dec 03 2008
MATHEMATICA
Select[Range[335], Mod @@ DivisorSigma[1, {#^2 + #, 2 # + 1}] == 0 &] (* Michael De Vlieger, Dec 14 2019 *)
PROG
(PARI) for(k=1, 335, if(!(sigma(k^2+k)%sigma(2*k+1)), print1(k, ", "))) \\ Hugo Pfoertner, Dec 10 2019
CROSSREFS
Cf. A000203.
Sequence in context: A163695 A134641 A162491 * A045350 A179273 A251964
KEYWORD
nonn
AUTHOR
J. M. Bergot, Nov 29 2008
EXTENSIONS
Corrected and extended by Emeric Deutsch and R. J. Mathar, Dec 03 2008
STATUS
approved

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Last modified April 23 12:44 EDT 2024. Contains 371913 sequences. (Running on oeis4.)