A067135 -id:A067135 - cp's OEIS frontend

A223091 Numbers k such that sigma(k - 2) = sigma(k + 2).

53, 68, 117, 222, 321, 1005, 2587, 4026, 4185, 4197, 5722, 5828, 5961, 8006, 8376, 11661, 12369, 12563, 13583, 14340, 15367, 16118, 17842, 18720, 20543, 25132, 29395, 30172, 32667, 36518, 39915, 40662, 42425, 42924, 47843, 49764, 50040, 50437, 52314, 53220

Offset: 1

Irina Gerasimova, Mar 22 2013

nonn

Corresponding values of sigma(n - 2) = sigma(n + 2): 72, 144, 144, 504, 360, 1080, 3456, 7560, 4320, 5040, 15120, 11664, .... The first two values not divisible by 72 are for n = 21 and 23, a(n) = 15367 and 17842, sigma = 21120 and 41664. A search up to a(n) = 10^8 did not turn up any sigma not divisible by 24. - Michael B. Porter, Mar 28 2013

			sigma(53 - 2) = sigma(53 + 2) = 72, sigma(68 - 2) = sigma(68 + 2) = 144, sigma(117 - 2) = sigma(117 + 2) = 144, sigma(222 - 2) = sigma(222 + 2) = 504, sigma(321 - 2) = sigma(321 + 2) = 360.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A067135, A175876.

Select[Range[10000], DivisorSigma[1, # - 2] == DivisorSigma[1, # + 2] &] (* Alonso del Arte, Mar 23 2013 *)
Flatten[Position[Partition[DivisorSigma[1,Range[55000]],5,1],?(#[[1]] == #[[5]]&),{1},Heads->False]]+2 (* _Harvey P. Dale, Sep 14 2016 *)

is(n)=sigma(n-2)==sigma(n+2) \\ Charles R Greathouse IV, Mar 17 2014

A067134 Numbers n such that sigma(n+1) = 2*sigma(n-1).

Original entry on oeis.org

119, 1559, 2939, 17759, 19919, 32219, 33839, 55964, 71039, 186779, 308039, 511499, 523775, 553499, 699359, 838214, 1048904, 1159379, 1328939, 1333247, 1700039, 2462687, 2703887, 2956079, 3115319, 3561095, 3764207, 3972695, 7625879, 7852919, 8048963

Offset: 1

Benoit Cloitre, Feb 18 2002

nonn

For each term given here, n+1 is divisible by 3, but that's not always true; n=12396999 is a counterexample.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A055574, A067135.

Flatten[Position[Partition[DivisorSigma[1,Range[8100000]],3,1],?(Last[#] == 2*First[#]&),{1},Heads->False]]+1 (* _Harvey P. Dale, Aug 19 2013 *)

s1=1; s2=3; for(n=2, 10^8, s3=sigma(n+1); if(s3==2*s1, print1(n ", ")); s1=s2; s2=s3) /* Donovan Johnson, Apr 06 2013 */

Edited by Dean Hickerson, Feb 20 2002

A217768 Smallest number k > 0 for which sigma(k - n) = sigma(k + n).

Original entry on oeis.org

34, 53, 23, 19, 26, 41, 31, 38, 49, 52, 68, 82, 112, 80, 103, 76, 110, 123, 4, 83, 101, 136, 3, 164, 130, 5, 147, 133, 381, 254, 7, 149, 253, 1, 131, 246, 172, 8, 404, 7, 6, 312, 148, 209, 309, 241, 487, 328, 9, 260

Offset: 1

Jayanta Basu, Mar 24 2013

nonn

The sigma() in the definition is the sum-of-divisors function A000203.

If m is negative, the definition uses the convention sigma(m) = sigma(-m).

			a(4) = 19 because sigma(19 + 4) = sigma(23) = 1 + 23 = 24 and sigma(19 - 4) = sigma(15) = 1 + 3 + 5 + 15 = 24 and there is no k < 19 for which sigma(k + 4) = sigma(k - 4).
a(26) = 5 because sigma(5 + 26) = sigma(31) = 1 + 31 = 32 and sigma(5 - 26) = sigma(-21) = sigma(21) = 1 + 3 + 7 + 21 = 32.

Cf. A067135, A175876, A223091.

Table[Min[Select[Range[500],DivisorSigma[1, # - n] == DivisorSigma[1, # + n] &]], {n,50}]

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A223091 Numbers k such that sigma(k - 2) = sigma(k + 2).

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A067134 Numbers n such that sigma(n+1) = 2*sigma(n-1).

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A217768 Smallest number k > 0 for which sigma(k - n) = sigma(k + n).

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