A175116 -id:A175116 - cp's OEIS frontend

A145470 A positive integer k is included if d(k) = d(k+1) + d(k+2), where d(k) is the number of divisors of k.

12, 30, 42, 45, 56, 66, 112, 220, 261, 282, 294, 297, 308, 342, 364, 390, 416, 477, 492, 513, 516, 532, 536, 555, 567, 572, 580, 620, 621, 632, 651, 700, 705, 768, 777, 786, 795, 812, 832, 836, 860, 880, 884, 891, 897, 906, 957, 975, 976, 981, 992, 1000, 1005

Offset: 1

Leroy Quet, Oct 11 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A145469, A175116.

Transpose[Select[Partition[Range[1010], 3, 1], DivisorSigma[0, First[#]] == DivisorSigma[0, Last[#]] + DivisorSigma[0, #[[2]]]&]][[1]] (* Amiram Eldar, Jul 17 2019 after Harvey P. Dale at A175116 *)

Extended by Ray Chandler, Oct 27 2008

A175115 An integer k, k >=3, is included if d(k) = d(k-1)*d(k-2), where d(k) is the number of divisors of k.

Original entry on oeis.org

3, 24, 120, 150, 195, 216, 294, 312, 399, 440, 459, 525, 540, 558, 570, 615, 630, 663, 693, 696, 744, 759, 774, 858, 999, 1032, 1095, 1125, 1152, 1176, 1239, 1350, 1455, 1470, 1494, 1608, 1624, 1659, 1664, 1710, 1725, 1734, 1785, 1860, 1880, 1896, 1914

Offset: 1

Leroy Quet, Feb 13 2010

nonn

Terms calculated by M. F. Hasler.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A175116, A145469.

Transpose[Select[Partition[Range[2000], 3, 1], DivisorSigma[0, Last[#]] == DivisorSigma[0, First[#]] * DivisorSigma[0, #[[2]]]&]][[1]] + 2 (* Amiram Eldar, Jul 17 2019 after Harvey P. Dale at A175116 *)

A190266 Numbers k such that tau(k-1) = (tau(k))^2 = tau(k+1), where tau(k) = A000005(k) (number of divisors of k).

Original entry on oeis.org

7, 1241, 1673, 1751, 1769, 2471, 2839, 3161, 3305, 3497, 3711, 4135, 4265, 4279, 4471, 4711, 5191, 5433, 5561, 6017, 6041, 6103, 6313, 6809, 6953, 7031, 7241, 7463, 7671, 8023, 8057, 8345, 8791, 8889, 9079, 10167, 10793, 10841, 11111, 11209, 11391, 11751, 12297, 12729

Offset: 1

Juri-Stepan Gerasimov, May 06 2011

nonn

			a(1)=7 because tau(6) = (tau(7))^2 = tau(8) = 4;
a(2)=1241 because tau(1240) = (tau(1241))^2 = tau(1242) = 16.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A074757, A090502. Subsequence of A036436.

Transpose[Select[Partition[Range[15000], 3, 1], DivisorSigma[0, #[[2]]]^2 == DivisorSigma[0, First[#]] == DivisorSigma[0, Last[#]]&]][[1]] + 1 (* Amiram Eldar, Jul 17 2019 after Harvey P. Dale at A175116 *)

isA190266(n)=my(t=numdiv(n-1)); issquare(t) & t==numdiv(n+1) & t==numdiv(n)^2 \\ Charles R Greathouse IV, May 14 2011

A000005(a(n)-1) = (A000005(a(n)))^2 = A000005(a(n)+1).

Data corrected by Amiram Eldar, Jul 17 2019

cp's OEIS Frontend

A145470 A positive integer k is included if d(k) = d(k+1) + d(k+2), where d(k) is the number of divisors of k.

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A175115 An integer k, k >=3, is included if d(k) = d(k-1)*d(k-2), where d(k) is the number of divisors of k.

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A190266 Numbers k such that tau(k-1) = (tau(k))^2 = tau(k+1), where tau(k) = A000005(k) (number of divisors of k).

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