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

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

1,1

Comments

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).

Links

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

Example

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

Mathematica

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

Crossrefs

Subsequence of A033996 and A351851.

Cf. A062327, A114617, A351854.

Sequence in context: A345832 A236891 A177217 * A274045 A277171 A258577

Adjacent sequences: A351849 A351850 A351851 * A351853 A351854 A351855

Keyword

nonn

Author

Amiram Eldar, Feb 22 2022

Status

approved