A351851 -id:A351851 - cp's OEIS frontend

A351853 Numbers that are divisible by the number of their divisors over the Eisenstein integers.

1, 2, 3, 6, 8, 24, 40, 80, 81, 88, 120, 128, 136, 162, 180, 184, 225, 232, 240, 264, 324, 328, 360, 376, 384, 408, 424, 448, 450, 472, 552, 560, 568, 625, 640, 648, 664, 696, 712, 756, 808, 856, 880, 896, 900, 904, 984, 1040, 1048, 1096, 1128, 1192, 1250, 1272

Offset: 1

Amiram Eldar, Feb 22 2022

nonn

Numbers k such that A319442(k) | k.

All the odd terms are squares or numbers of the form 3 times a square.

			6 is a term since it is divisible by A319442(6) = 6.

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

Cf. A033950, A048166, A319442, A351851.

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]]; Select[Range[1000], q]

A351852 Numbers k such that k and k+1 are both divisible by the number of their divisors over the Gaussian integers.

Original entry on oeis.org

31328, 173888, 893024, 1734488, 1896128, 4322240, 5405624, 8485568, 8982008, 9345248, 21874328, 38750624, 78588224, 137663288, 139074848, 189035000, 198387224, 270174968, 281333528, 290873024, 315950624, 326271968, 340513208, 357096608, 499656608, 584527328, 693637568

Offset: 1

Amiram Eldar, Feb 22 2022

nonn

Numbers k such that A062327(k) | k and A062327(k+1) | k+1.

All the terms are even numbers of the form k^2 - 1 (A033996).

			31328 is a term since 31328 is divisible by A062327(31328) = 88 and 31329 is divisible by A062327(31329) = 9.

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

Subsequence of A033996 and A351851.

Cf. A062327, A114617, A351854.

q[n_] := Divisible[n, DivisorSigma[0, n, GaussianIntegers -> True]]; Select[Range[1, 3*10^4, 2]^2 - 1, q[#] && q[# + 1] &]

cp's OEIS Frontend

A351853 Numbers that are divisible by the number of their divisors over the Eisenstein integers.

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