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

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

Author

Jianing Song, Dec 19 2020

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A005179, A328897.

Programs

PARI

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