A335328 - OEIS

%I #22 Jun 05 2020 12:47:44

%S 135,296,343,375,1160,1431,1592,1624,2295,2456,2727,3429,3591,3624,

%T 3752,3992,4023,4184,4887,4913,5048,5144,5319,5480,6183,6344,6375,

%U 6858,7479,7624,7640,7749,7911,8072,8375,8936,9207,9368,9624,10071,10232,10375,10503,10632

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

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

%H Amiram Eldar, <a href="/A335328/b335328.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

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

%t 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

%Y Subsequence of A048109 and A000037.

%Y Cf. A000005, A034444, A048105.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jun 01 2020