A383391 -id:A383391 - cp's OEIS frontend

A383390 Numbers k such that k^2 and (k+1)^2 are both abundant numbers.

104, 495, 584, 735, 944, 1155, 1364, 1484, 2144, 2204, 2415, 2624, 2924, 2925, 3135, 3255, 3794, 3795, 4304, 4484, 4784, 4844, 5264, 5355, 5445, 5564, 5565, 5655, 5775, 5984, 6104, 6764, 7424, 7455, 7664, 7755, 7875, 8084, 8294, 8295, 8414, 8415, 8924, 9009, 9344, 9944, 9975

Offset: 1

Amiram Eldar, Apr 25 2025

nonn

The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 5, 47, 459, 4655, 46733, 460693, 4612685, 46177602, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00461... .

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

Subsequence of A381738.
A383391 and A096399 are subsequences.
Cf. A005101, A063734.

Select[Range[10000], DivisorSigma[-1, #^2] > 2 && DivisorSigma[-1, (#+1)^2] > 2 &]

is1(k) = {my(f = factor(k)); prod(i = 1, #f~, f[i,2] *= 2); sigma(f, -1) > 2;}
list(lim) = {my(q1 = is1(1), q2); for(k = 2, lim, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

cp's OEIS Frontend

A383390 Numbers k such that k^2 and (k+1)^2 are both abundant numbers.

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