A175876 -id:A175876 - 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

A175874 a(n) = least number such that sigma(a(n)+n)=n*sigma(a(n)).

Original entry on oeis.org

14, 118, 3, 2

Offset: 1

Zak Seidov, Oct 06 2010

a(1)= A002961(1).
a(2)= A175876(1), a(3)= A175875(1). - Zak Seidov, Jul 07 2013
Is n = 2 the only solution for sigma(n+4)=4*sigma(n)? - Zak Seidov, Jul 07 2013
A further solution to sigma(n+4)=4*sigma(n), and the terms a(5) and a(6), if they exist, they are all larger than 3*10^12. - Giovanni Resta, Jun 06 2016

			sigma(14+1)/sigma(14)=24/24=1, sigma(118+2)/sigma(118)=360/180=2,
sigma(3+3)/sigma(3)=12/4=3, sigma(4+4)/sigma(2)=12/3=4.

Cf. A000203 sigma(n), A002961 sigma(n) = sigma(n+1).

Cf. A175875, A175876. - Zak Seidov, Jul 07 2013

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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A175874 a(n) = least number such that sigma(a(n)+n)=n*sigma(a(n)).

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

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