A350090 -id:A350090 - cp's OEIS frontend

A350120 a(n) is the least integer k such that A350090(k) = 2*n-1 or -1 if no such k exists.

1, 5, 22, 33, 5951, 124, 90088, 187, 757, 1149, 237152823, 852, 30744479715, 207737, 15555, 876, 40828735337636, 1541, 2932093694892923, 8454, 3557030, 802103321, 1895798161468690610

Offset: 1

Michel Marcus, Dec 15 2021

Most terms of A350090 are odd. It is conjectured by Klaus Purath that all odd numbers appear in A350090.
a(n) is the least k such that tau(3*k*(k+1)+1) = 2*n. - Jinyuan Wang, Dec 19 2021
a(11) >= 10^8 if it exists. - Michel Marcus, Dec 20 2021

Cf. A000005 (tau), A002378, A003215, A350090.

a(n) = my(k=1, m=2*n); while (numdiv(3*k*(k+1)+1) != m, k++); k; \\ Michel Marcus, Dec 20 2021

a(11)-a(23) from Klaus Purath, Jan 04 2022

A350192 Distinct values of A350090 in the order in which they appear.

Original entry on oeis.org

0, 1, 3, 2, 5, 7, 11, 15, 17, 23, 31, 19, 35, 9, 47, 39, 63, 29, 26, 95, 53, 71, 143, 13, 79, 127, 27, 59, 107, 191, 159, 287, 55, 255, 167, 99, 119, 111, 319, 83, 41, 215, 383, 179, 49, 239, 431, 89, 323, 511, 223, 359, 575, 479, 485, 639, 87, 161, 767, 80, 335

Offset: 1

Michel Marcus, Dec 19 2021

nonn

Cf. A002378, A003215, A350090, A350120, A350193.

a(1) = 0 inserted by and more terms from Jinyuan Wang, Dec 19 2021

A350193 Indices that give distinct values of A350090 in the order in which they appear.

Original entry on oeis.org

0, 1, 5, 7, 22, 33, 124, 187, 757, 852, 876, 1149, 1541, 5951, 6767, 8454, 10067, 15555, 20272, 29751, 51721, 59662, 89055, 90088, 92489, 161673, 207737, 217341, 225622, 361054, 452639, 530990, 560684, 669999, 733454, 1000067, 1866828, 2090121, 2464677, 3148962

Offset: 1

Michel Marcus, Dec 19 2021

nonn

Cf. A002378, A003215, A350090, A350120, A350192.

With[{s = Table[Count[Range[0, n - 1], ?(IntegerQ@ Sqrt[4 # + 1] &[(3 n (n + 1) + 1) - (3 # (# + 1) + 1)] &)], {n, 0, 2^10}]}, Map[-1 + FirstPosition[s, #][[1]] &, DeleteDuplicates@ s]] (* _Michael De Vlieger, Dec 19 2021, after Amiram Eldar at A350090 *)

a(1) = 0 inserted by and more terms from Jinyuan Wang, Dec 19 2021

cp's OEIS Frontend

A350120 a(n) is the least integer k such that A350090(k) = 2*n-1 or -1 if no such k exists.

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A350192 Distinct values of A350090 in the order in which they appear.

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Author

Keywords

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Extensions

A350193 Indices that give distinct values of A350090 in the order in which they appear.

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Author

Keywords

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Mathematica

Extensions