A339863 -id:A339863 - cp's OEIS frontend

A349940 Terms of A339863 that are congruent to 5 modulo 6: numbers k == 5 (mod 6) such that A005179(k-1) > A005179(k) < A005179(k+1) >A005179(k+2) < A005179(k+3).

425, 845, 1265, 1643, 1925, 2525, 2873, 3335, 3395, 3575, 3683, 3971, 4163, 4307, 4343, 4475, 4613, 4667, 4805, 5141, 5285, 5423, 5603, 5945, 6095, 6305, 6683, 6851, 6875, 6893, 6923, 7337, 7661, 7733, 7973, 8075, 8303, 8393, 8453, 8723, 8825, 9191, 9425, 9581, 9821, 9875

Offset: 1

Jianing Song, Dec 05 2021

nonn

Numbers k such that both k and k+2 are in A349939.

Numbers k == 5 (mod 6) such that, the smallest number with exactly k divisors is smaller than the smallest number with exactly k-1 or k+1 divisors, and that the smallest number with exactly k+2 divisors is smaller than the smallest number with exactly k+1 or k+3 divisors.

			The smallest numbers with exactly 424, 425, 426, 427 and 428 divisors are 472877960873902080, 3317760000, 53126622932283508654080, 840479776858391445504 and 1216944576219100225436835077160960 respectively. The smallest number with exactly 425 divisors is smaller than the smallest number with exactly 424 or 426 divisors, the smallest number with exactly 427 divisors is smaller than the smallest number with exactly 426 or 428 divisors, and 425 == 5 (mod 6), so 425 is a term.

Matthew House, Table of n, a(n) for n = 1..10000

Cf. A005179, A339863, A349939.

isA349940(k) = if(k%6==5, my(v=vector(5, n, A005179(k-2+n))); v[2]A005179 for its program

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

Original entry on oeis.org

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

Jianing Song, Oct 30 2019

nonn

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.

			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.

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

Cf. A005179, A339863.

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

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

cp's OEIS Frontend

A349940 Terms of A339863 that are congruent to 5 modulo 6: numbers k == 5 (mod 6) such that A005179(k-1) > A005179(k) < A005179(k+1) >A005179(k+2) < A005179(k+3).

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