A350800 Numbers k such that k and k+1 have the same number and sum of divisors but a different number of distinct prime factors.

64665, 109214, 2305557, 4701537, 6444873, 10118654, 32225337, 33876117, 70282053, 105967784, 149205914, 187434621, 268890218, 279113505, 334925577, 357340922, 391392134, 424942604, 575712494, 610752933, 612863198, 641703842, 701792234, 743194142, 800679495

Offset: 1

Author

Kevin P. Thompson, Jan 16 2022

Keywords

• nonn

Comments

Subsequence of A054004. Most members of A054004 are not a part of this subsequence, so consecutive numbers with equal tau and sigma most often achieve this with an equal count of distinct prime factors.

Examples

			64665 is a term of this sequence since tau(64665) = tau(64666) = 8 and sigma(64665) = sigma(64666) = 2160, but omega(64665) = 4 and omega(64666) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..223 (terms 1..106 from Kevin P. Thompson)

Crossrefs

Cf. A000005, A000203, A001221, A054004.

Programs

Mathematica

Select[Range[10^7], DivisorSigma[{0, 1}, #] ==  DivisorSigma[{0, 1}, # + 1] && PrimeNu[#] != PrimeNu[# + 1] &] (* Amiram Eldar, Jan 20 2022 *)