A054004
Numbers k such that k and k+1 have the same number and sum of divisors.
Original entry on oeis.org
14, 1334, 1634, 2685, 33998, 42818, 64665, 84134, 109214, 122073, 166934, 289454, 383594, 440013, 544334, 605985, 649154, 655005, 792855, 1642154, 2284814, 2305557, 2913105, 3571905, 3682622, 4701537, 5181045, 6431732
Offset: 1
Divisors of 14 = {1, 2, 7, 14}, divisors of 15 = {1, 3, 5, 15}, both have four divisors and sum = 24.
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Select[Range[100000], DivisorSigma[0, #] == DivisorSigma[0, # + 1] && DivisorSigma[1, #] == DivisorSigma[1, # + 1] &] (* Jayanta Basu, Mar 20 2013 *)
A054005
Sum of divisors of k such that k and k+1 have the same number and sum of divisors.
Original entry on oeis.org
24, 2160, 2640, 4320, 51840, 65280, 115200, 138240, 194400, 186048, 276480, 483840, 622080, 700416, 950400, 984960, 1118880, 1128960, 1612800, 2661120, 3937248, 3617280, 5019840, 6128640, 5806080, 7375680, 8467200, 11583936
Offset: 1
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Select[Partition[Table[{n,DivisorSigma[0,n],DivisorSigma[1,n]},{n,116*10^5}],2,1],#[[1,2]]== #[[2,2]] && #[[1,3]]==#[[2,3]]&][[All,1,3]] (* Harvey P. Dale, May 16 2023 *)
A054007
Numbers k such that k and k+1 have the same sum but an unequal number of divisors.
Original entry on oeis.org
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
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
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Select[Range[100000], DivisorSigma[0, #] != DivisorSigma[0, # + 1] && DivisorSigma[1, #] == DivisorSigma[1, # + 1] &] (* Jayanta Basu, Mar 20 2013 *)
Showing 1-3 of 3 results.