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

Author

Zak Seidov and Amiram Eldar, Jun 06 2020

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A048109, A335328, A335397 and A335398.

Cf. A000005, A034444, A048105.

Programs

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