A351853 -id:A351853 - cp's OEIS frontend

A351851 Numbers that are divisible by the number of their divisors over the Gaussian integers.

1, 6, 9, 18, 20, 56, 126, 168, 180, 198, 280, 342, 352, 414, 432, 441, 486, 504, 558, 616, 625, 728, 774, 832, 846, 952, 1056, 1062, 1064, 1089, 1176, 1206, 1278, 1288, 1422, 1494, 1512, 1624, 1736, 1760, 1848, 1854, 1920, 1926, 2025, 2072, 2160, 2286, 2296, 2358

Offset: 1

Amiram Eldar, Feb 22 2022

nonn

Numbers k such that A062327(k) | k.

All the odd terms are squares.

			6 is a term since it is divisible by A062327(6) = 6.

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

Cf. A033950, A048166, A062327, A351853.

Select[Range[2400], Divisible[#, DivisorSigma[0, #, GaussianIntegers -> True]] &]

A351854 Numbers k such that k and k+1 are both divisible by the number of their divisors over the Eisenstein integers.

Original entry on oeis.org

1, 2, 80, 3968, 50624, 497024, 505520, 3207680, 6890624, 9150624, 12383360, 12852224, 13549760, 19210688, 20657024, 25250624, 41796224, 41873840, 47900240, 48650624, 79121024, 81450624, 86099840, 132503120, 140920640, 149450624, 174636224, 186732224, 214769024

Offset: 1

Amiram Eldar, Feb 22 2022

nonn

Numbers k such that A319442(k) | k and A319442(k+1) | k+1.

Except for 1 and 2, all the terms are even numbers of the form k^2 - 1 (A033996).

			2 is a term since 2 is divisible by A319442(2) = 2 and 3 is divisible by A319442(3) = 3.
80 is a term since 80 is divisible by A319442(80) = 10 and 81 is divisible by A319442(81) = 9.

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

Subsequence of A351853.

Cf. A033996, A114617, A319442, A351852.

f[p_, e_] := Switch[Mod[p, 3], 0, 2*e + 1, 1, (e + 1)^2, 2, e + 1]; eisNumDiv[1] = 1; eisNumDiv[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := Divisible[n, eisNumDiv[n]]; Join[{1, 2}, Select[Range[3, 15000, 2]^2 - 1, q[#] && q[# + 1] &]]

cp's OEIS Frontend

A351851 Numbers that are divisible by the number of their divisors over the Gaussian integers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica