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

1,1

Comments

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

Links

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

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

Example

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

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

Crossrefs

Subsequence of A048109 and A000037.

Cf. A000005, A034444, A048105.

Sequence in context: A342189 A176313 A372691 * A215173 A225360 A328651

Adjacent sequences: A335325 A335326 A335327 * A335329 A335330 A335331

Keyword

nonn

Author

Amiram Eldar, Jun 01 2020

Status

approved