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
Examples
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.
Programs
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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
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
Comments