A054007 Numbers k such that k and k+1 have the same sum but an unequal number of divisors.

206, 957, 1364, 2974, 4364, 14841, 18873, 19358, 20145, 24957, 36566, 56564, 74918, 79826, 79833, 92685, 111506, 116937, 138237, 147454, 161001, 162602, 174717, 190773, 193893, 201597, 230390, 274533, 347738, 416577, 422073, 430137

Offset: 1

Author

Asher Auel, Jan 12 2000

Keywords

• nonn

Examples

			The divisors of 206 are 1, 2, 103, 206, so tau(206) = 4 and sigma(206) = 312; the divisors of 207 are 1, 3, 9, 23, 69, 207, so tau(207) = 6 and sigma(207) = 312. Hence, the integer 206 belongs to this sequence. - _Bernard Schott_, Oct 18 2019
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..8304 (terms below 10^13, calculated from the b-file at A002961)

Crossrefs

Cf. A000005, A000203, A002961, A005237, A053249, A054004, A054005, A054006.

Programs

Mathematica

Select[Range[100000], DivisorSigma[0, #] != DivisorSigma[0, # + 1] && DivisorSigma[1, #] == DivisorSigma[1, # + 1] &] (* Jayanta Basu, Mar 20 2013 *)

Formula

Members of A002961 which are not members of A054004

Extensions

More terms from Jud McCranie, Oct 15 2000