A335399 Starts of runs of 5 consecutive numbers that have an equal number of unitary and nonunitary divisors (A048109).

146447622, 2259799749, 2559357269, 2647718871, 3660580374, 4262858871, 4708102374, 5188831623, 5341658373, 5494129749, 5728055749, 5876715750, 6127708374, 6455588247, 6608437623, 6612840374, 6617111750, 6689113623, 6722600373, 7456747623, 7923798375, 8272111445

Offset

1,1

Comments

Do longer runs of consecutive numbers with an equal number of unitary and nonunitary divisors exist for any length of run?

Starts of runs of 6 consecutive numbers that have an equal number of unitary and nonunitary divisors, from Giovanni Resta's bfile, 80566783622, 117243671750, 390773539750, 573122731621, 636972066374. - Zak Seidov, Jun 07 2020

Links

Giovanni Resta, Table of n, a(n) for n = 1..3000

Example

146447622 is a term since 146447622, 146447623, 146447624, 146447625 and 146447626 each have an equal number of unitary and nonunitary divisors. 146447622 has 32 unitary divisors and 32 nonunitary divisors, 146447623, 146447625 and 146447626 each have 8 and 8, and 146447624 has 16 and 16.

Mathematica

q[n_] := DivisorSigma[0, n] == 2^(PrimeNu[n] + 1); v = q /@ Range[5]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 4]], {k, 6, 3*10^8}]; seq

Crossrefs

Subsequence of A048109, A335328, A335397 and A335398.

Cf. A000005, A034444, A048105.

Sequence in context: A224638 A224642 A185855 * A226970 A212470 A180345

Adjacent sequences: A335396 A335397 A335398 * A335400 A335401 A335402

Keyword

nonn

Author

Zak Seidov and Amiram Eldar, Jun 06 2020

Status

approved