

A335328


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


5



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
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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, n1]]; q1 = q2, {n, 2, 10^4}]; s


CROSSREFS

Subsequence of A048109 and A000037.
Cf. A000005, A034444, A048105.
Sequence in context: A325569 A342189 A176313 * A215173 A225360 A328651
Adjacent sequences: A335325 A335326 A335327 * A335329 A335330 A335331


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jun 01 2020


STATUS

approved



