A062327 -id:A062327 - cp's OEIS frontend

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

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] &]

A125271 Number of Gaussian integer divisors of n (having positive real part).

Original entry on oeis.org

1, 4, 2, 7, 6, 8, 2, 10, 3, 20, 2, 14, 6, 8, 12, 13, 6, 12, 2, 34, 4, 8, 2, 20, 15, 20, 4, 14, 6, 40, 2, 16, 4, 20, 12, 21, 6, 8, 12, 48, 6, 16, 2, 14, 18, 8, 2, 26, 3, 48, 12, 34, 6, 16, 12, 20, 4, 20, 2, 68, 6, 8, 6, 19, 28, 16, 2, 34, 4, 40, 2, 30, 6, 20, 30

Offset: 1

Mitch Cervinka (puritan(AT)toast.net), Jan 16 2007

To avoid the redundancy of counting the negatives of the divisors, we consider only divisors having a positive real part.

The usual method of counting complex divisors is to exclude associates. For example, although 1+i and 1-i both divide 2, one is just -i times the other. This sequence counts each first-quadrant complex divisor twice. Sequence A062327 counts those complex divisors only once. - T. D. Noe, Feb 21 2007

			a(5) = 6 because 5 is divisible by the Gaussian integers {1, 1-2i, 1+2i, 2-i, 2+i, 5}, which is 6 divisors in all.

Eric Weisstein's World of Mathematics, Gaussian Integer.

Cf. A000005, A062327.

a(n) = 2*A062327(n) - A000005(n). - T. D. Noe, Feb 21 2007

cp's OEIS Frontend

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

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