A328897 -id:A328897 - cp's OEIS frontend

A349939 Terms in A328897 that are not divisible by 3: numbers k > 1 not divisible by 2 or 3 such that A005179(k-1) > A005179(k) < A005179(k+1).

187, 245, 275, 403, 425, 427, 437, 473, 583, 605, 637, 665, 731, 763, 775, 805, 845, 847, 875, 893, 931, 1003, 1075, 1085, 1127, 1183, 1235, 1265, 1267, 1309, 1357, 1375, 1397, 1421, 1435, 1445, 1463, 1525, 1547, 1573, 1577, 1615, 1625, 1643, 1645, 1705, 1757

Offset: 1

Jianing Song, Dec 05 2021

nonn

Numbers k not divisible by 2 or 3 such that, the smallest number with exactly k divisors is smaller than the smallest number with exactly k-1 or k+1 divisors.

			The smallest numbers with exactly 186, 187 and 188 divisors are 48318382080, 3869835264 and 1055531162664960 respectively. The smallest number with exactly 187 divisors is smaller than the smallest number with exactly 186 or 188 divisors, and 187 is not divisible by 2 or 3, so 187 is a term.
The smallest numbers with exactly 244, 245 and 246 divisors are 17293822569102704640, 29160000 and 49478023249920 respectively. The smallest number with exactly 245 divisors is smaller than the smallest number with exactly 244 or 246 divisors, and 245 is not divisible by 2 or 3, so 245 is a term.

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

Cf. A005179, A328897, A349940.

isA349939(k) = (k%2&&k%3&&k>1) && A005179(k)<A005179(k-1) && A005179(k)<A005179(k+1) \\ See A005179 for its program

A339863 Odd numbers k > 1 such that A005179(k-1) > A005179(k) < A005179(k+1) > A005179(k+2) < A005179(k+3).

Original entry on oeis.org

187, 243, 403, 423, 425, 427, 435, 583, 663, 729, 763, 775, 845, 891, 1003, 1083, 1125, 1265, 1267, 1375, 1395, 1419, 1545, 1573, 1575, 1615, 1643, 1645, 1755, 1771, 1813, 1843, 1885, 1925, 1953, 2035, 2275, 2385, 2403, 2523, 2525, 2533, 2635, 2673, 2695

Offset: 1

Jianing Song, Dec 19 2020

nonn

Odd numbers k such that k and k+2 are both in A328897.

Despite the fact that only square numbers have an odd number of divisors, there are surprisingly many terms here. The numbers of terms below 10^3, 10^4 and 10^5 are 14, 208 and 3004 respectively.

			The smallest numbers with exactly 582, 583, 584, 585 and 586 divisors are ~3.565*10^30, ~2.659*10^20, ~4.958*10^24, 406425600 and ~2.387*10^88 respectively. We have A005179(582) > A005179(583) < A005179(584) > A005179(585) < A005179(586), hence 583 is a term.

Matthew House, Table of n, a(n) for n = 1..10000 (terms 1..3004 below 10^5 from Jianing Song)

Cf. A005179, A328897.

isA339863(k) = if(k%2&&k>1, my(v=vector(5, n, A005179(k-2+n))); v[2]

cp's OEIS Frontend

A349939 Terms in A328897 that are not divisible by 3: numbers k > 1 not divisible by 2 or 3 such that A005179(k-1) > A005179(k) < A005179(k+1).

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