A369155 Numbers k such that d(k) < d(k - 1) and d(k) < d(k + 1), and d(k) is also a record for this type of number where d(k) is the number of divisors of k.

5, 9, 51, 153, 351, 3249, 6579, 19551, 47151, 122451, 246975, 393471, 3292289, 10792495, 15270849, 25770879, 58967271, 60642945, 242340175, 481701375, 5122147185, 6644739375, 6971026699, 21061868751, 92330654625, 213089528575, 1159484186575, 1305664357375

Offset

1,1

Comments

Numbers in A075025 with record number of divisors.

Links

Table of n, a(n) for n=1..28.

Example

351 is a term in this sequence because d(351) = 8, d(350) = 12, and d(352) = 12, so 351 is a number that has fewer divisors than each of its neighbors, but no number below 351 has that property and has at least 8 divisors.

Prog

(PARI) lista(kmax) = my(d1 = numdiv(1), d2 = numdiv(2), d3, dm = 0); for(k = 3, kmax, d3 = numdiv(k); if(d2 < d1 && d2 < d3 && d2 > dm, print1(k-1, ", "); dm = d2); d1 = d2; d2 = d3); \\ Amiram Eldar, Jan 16 2024

Crossrefs

Cf. A000005. Subsequence of A075025.

Sequence in context: A289909 A000324 A123817 * A124421 A262918 A283918

Adjacent sequences: A369152 A369153 A369154 * A369156 A369157 A369158

Keyword

nonn,hard

Author

Zhicheng Wei, Jan 14 2024

Extensions

a(9)-a(20) from Michel Marcus, Jan 15 2024

a(21)-a(22) from Amiram Eldar, Jan 16 2024

a(23)-a(28) from Martin Ehrenstein, Feb 08 2024

Status

approved