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).

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

Offset

1,1

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A152213 A152214 A152215 * A152217 A152218 A152219

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