A335328 Number k such that both k and k+1 have an equal number of unitary and nonunitary divisors.

135, 296, 343, 375, 1160, 1431, 1592, 1624, 2295, 2456, 2727, 3429, 3591, 3624, 3752, 3992, 4023, 4184, 4887, 4913, 5048, 5144, 5319, 5480, 6183, 6344, 6375, 6858, 7479, 7624, 7640, 7749, 7911, 8072, 8375, 8936, 9207, 9368, 9624, 10071, 10232, 10375, 10503, 10632

Offset: 1

Author

Amiram Eldar, Jun 01 2020

Keywords

• nonn

Comments

Terms k such that k+1 is also in this sequence are 22625, 28375, 40472, ...

Examples

			135 is a term since both 135 and 136 have 4 unitary divisors and 4 nonunitary divisors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A048109 and A000037.

Cf. A000005, A034444, A048105.

Programs

Mathematica

seqQ[n_] := DivisorSigma[0, n] == 2^(PrimeNu[n] + 1); q1 = seqQ[1]; s = {}; Do[q2 = seqQ[n]; If[q1 && q2, AppendTo[s, n-1]]; q1 = q2, {n, 2, 10^4}]; s

Formula

Numbers n such that both n and n+1 are of the form p^3 * q * r * s * ... where p, q, r, ... are distinct primes (with zero or more primes q, r, s, ...). - Charles R Greathouse IV, Jun 05 2020