A328897 Odd numbers k > 1 such that A005179(k-1) > A005179(k) < A005179(k+1).

27, 45, 75, 105, 117, 135, 147, 165, 187, 189, 231, 243, 245, 275, 285, 297, 315, 333, 345, 357, 375, 387, 403, 405, 423, 425, 427, 429, 435, 437, 459, 473, 495, 507, 525, 555, 567, 583, 585, 605, 621, 627, 637, 663, 665, 675, 693, 729, 731, 735, 741, 763, 765, 775, 777, 795

Offset

1,1

Comments

As only square numbers have an odd number of divisors, for odd k, A005179(k) is usually larger than either A005179(k-1) or A005179(k+1) (or both). This sequence lists the exceptions. There are 71 terms below 10^3, 963 terms below 10^4, 11179 terms below 10^5. It seems that the density of this sequence over all the odd numbers is > 0.2.

Is there any odd k such that A005179(k) is smaller than A005179(k-3), A005179(k-1), A005179(k+1) and A005179(k+3)? There is no such k < 10^5.

Links

Jianing Song, Table of n, a(n) for n = 1..11179 (all terms below 10^5)

Example

27 is a term because the smallest number with 27 divisors is 900, which is smaller than both A005179(26) = 12288 and A005179(28) = 960, so 27 is a term.
45 is a term because the smallest number with 45 divisors is 3600, which is smaller than both A005179(44) = 15360 and A005179(46) = 12582912, so 45 is a term.

Maple

A := [seq(A005179(n), n=1..800)];
isA := k -> k::odd and A[k] < A[k-1] and A[k] < A[k+1]:
select(isA, [$3..799]); # Peter Luschny, Oct 30 2019

Prog

(PARI) isA328897(k) = (k%2&&k>1) && A005179(k)<A005179(k-1) && A005179(k)<A005179(k+1) \\ Corrected by Jianing Song, Dec 05 2021

Crossrefs

Cf. A005179, A339863.

Sequence in context: A046373 A228057 A113481 * A369979 A039325 A043148

Adjacent sequences: A328894 A328895 A328896 * A328898 A328899 A328900

Keyword

nonn

Author

Jianing Song, Oct 30 2019

Status

approved