

A225211


Numbers n such that sigma(n+1)  sigma(n) divides n.


1



2, 3, 4, 7, 8, 20, 26, 31, 127, 532, 954, 2186, 2524, 8191, 104944, 131071, 524287, 918080, 1594322, 10368512, 26100416, 2147483647, 24708617408, 25316030960, 35053995440, 45883878740
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OFFSET

1,1


COMMENTS

Supersequence of A000668 (Mersenne primes) and A067803 (numbers n such that sigma(n)  sigma(n+1) = n).
Corresponding integers k such that sigma(n+1)  sigma(n) = n/k: 2, 1, 4, 1, 4, 2, 13, 1, 1, 1, 1, 1093, 2, 1, ....
a(27) > 10^11.  Donovan Johnson, May 04 2013
a(27) > 10^13.  Giovanni Resta, Aug 01 2013


LINKS

Table of n, a(n) for n=1..26.


EXAMPLE

Number 2186 is in sequence because sigma(2187)  sigma(2186) = 3280  3282 = 2 which divides 2186.


MATHEMATICA

Select[Range[1000000], DivisorSigma[1, # + 1]  DivisorSigma[1, #] != 0 && IntegerQ[#/(DivisorSigma[1, # + 1]  DivisorSigma[1, #])] &] (* T. D. Noe, May 02 2013 *)
Select[Partition[Table[{n, DivisorSigma[1, n]}, {n, 16*10^5}], 2, 1], Divisible[#[[1, 1]], #[[1, 2]]#[[2, 2]]]&][[All, 1, 1]]//Quiet (* Harvey P. Dale, Jun 27 2020 *)


PROG

(PARI) is(n)=my(m=sigma(n+1)sigma(n)); m && n%m==0 \\ Charles R Greathouse IV, May 02 2013


CROSSREFS

Cf. A000203, A000668, A067803.
Sequence in context: A334020 A006549 A134459 * A159554 A256606 A101128
Adjacent sequences: A225208 A225209 A225210 * A225212 A225213 A225214


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, May 01 2013


EXTENSIONS

a(15)a(21) from Charles R Greathouse IV, May 02 2013
a(22)a(26) from Donovan Johnson, May 04 2013


STATUS

approved



