A054007 -id:A054007 - cp's OEIS frontend

A054004 Numbers k such that k and k+1 have the same number and sum of divisors.

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

Asher Auel, Jan 12 2000

nonn

			Divisors of 14 = {1, 2, 7, 14}, divisors of 15 = {1, 3, 5, 15}, both have four divisors and sum = 24.

Amiram Eldar, Table of n, a(n) for n = 1..1831 (calculated using the b-file at A002961; terms 1..967 from T. D. Noe)

Cf. A000005, A000203, A002961, A005237, A053249, A054005, A054006, A054007.

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

More terms from Jud McCranie, Jun 02 2000

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

Asher Auel, Jan 12 2000

nonn

			See example in A054004.

Amiram Eldar, Table of n, a(n) for n = 1..1831

Cf. A000005, A000203, A002961, A005237, A053249, A054004, A054006, A054007.

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 *)

a(n) = sigma(A054004(n)).

More terms from Jud McCranie, Oct 15 2000

Definition clarified by Harvey P. Dale, May 16 2023

A054006 Number of divisors of k and k+1 which have the same number and sum of divisors.

Original entry on oeis.org

4, 8, 8, 8, 8, 8, 16, 16, 16, 8, 16, 16, 16, 16, 16, 16, 16, 16, 32, 16, 16, 16, 16, 32, 16, 16, 16, 24, 16, 16, 16, 32, 32, 32, 16, 16, 32, 16, 32, 16, 16, 32, 32, 16, 32, 16, 16, 16, 16, 16, 32, 32, 16, 32, 16, 16, 64, 32, 16, 32, 16, 32, 16, 64, 32, 32, 16, 32, 32, 32, 32

Offset: 1

Asher Auel, Jan 12 2000

nonn

			See example in A054004.

Amiram Eldar, Table of n, a(n) for n = 1..1831 (calculated using the b-file at A054004)

Cf. A000005, A000203, A002961, A005237, A053249, A054004, A054005, A054007.

Select[Partition[Array[DivisorSigma[{0, 1}, #] &, 10^6], 2, 1], SameQ @@ # &][[All, 1, 1]] (* Michael De Vlieger, Nov 21 2019 *)

a(n) = tau(A054004(n)).

More terms from Jud McCranie, Oct 15 2000

cp's OEIS Frontend

A054004 Numbers k such that k and k+1 have the same number and sum of divisors.

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A054005 Sum of divisors of k such that k and k+1 have the same number and sum of divisors.

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A054006 Number of divisors of k and k+1 which have the same number and sum of divisors.

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