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

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

Author

Jayanta Basu, Mar 24 2013

Keywords

• nonn

Comments

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).

Examples

			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.
		

Crossrefs

Cf. A067135, A175876, A223091.

Programs

Mathematica

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