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A335399
Starts of runs of 5 consecutive numbers that have an equal number of unitary and nonunitary divisors (A048109).
2
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
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.
Sequence in context: A224638 A224642 A185855 * A226970 A212470 A180345
KEYWORD
nonn
AUTHOR
Zak Seidov and Amiram Eldar, Jun 06 2020
STATUS
approved