A225211 Numbers n such that sigma(n+1) - sigma(n) divides n.

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

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 *)
Position[MapIndexed[Divisible[#2[[1]], #] &, Subtract @@@ Partition[DivisorSigma[1, Range[10^6]], 2, 1]], True] // Flatten // Quiet (* Eric W. Weisstein, Dec 21 2023 *)

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