A333052 Numbers m such that d(m) = d(m+1) and d(k) < d(m) for all k < m such that d(k) = d(k+1), where d(m) is the number of divisors of m (A000005).

2, 14, 44, 104, 735, 2295, 5264, 5984, 21735, 201824, 3341624, 6481475, 7316000, 49727600, 103488384, 205684479, 349167104, 391738599, 1921172175, 6110171144, 7616307699

Offset: 1

Author

Amiram Eldar, Mar 06 2020

Keywords

• nonn
• more

Comments

The corresponding numbers of divisors are 2, 4, 6, 8, 12, 16, 20, 24, 32, 48, 64, 72, 96, 120, 128, 144, 160, 192, 240, 256, 288, ...

Examples

			2 is a term since (2, 3) is the first pair of consecutive numbers with the same number of divisors: d(2) = d(3) = 2.
14 is a term since d(14) = d(15) = 4 > d(2) = 2.
44 is a term since d(44) = d(45) = 6 > d(14) = 4.
		

Crossrefs

Cf. A000005, A002182, A005237, A175143.

Programs

Mathematica

seq = {}; dmax = 0; d1 = 1; Do[If[d1 == (d2 = DivisorSigma[0, n]) && d1 > dmax, dmax = d1; AppendTo[seq, n-1]]; d1 = d2, {n, 2, 10^4}]; seq