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A350800
Numbers k such that k and k+1 have the same number and sum of divisors but a different number of distinct prime factors.
1
64665, 109214, 2305557, 4701537, 6444873, 10118654, 32225337, 33876117, 70282053, 105967784, 149205914, 187434621, 268890218, 279113505, 334925577, 357340922, 391392134, 424942604, 575712494, 610752933, 612863198, 641703842, 701792234, 743194142, 800679495
OFFSET
1,1
COMMENTS
Subsequence of A054004. Most members of A054004 are not a part of this subsequence, so consecutive numbers with equal tau and sigma most often achieve this with an equal count of distinct prime factors.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..223 (terms 1..106 from Kevin P. Thompson)
EXAMPLE
64665 is a term of this sequence since tau(64665) = tau(64666) = 8 and sigma(64665) = sigma(64666) = 2160, but omega(64665) = 4 and omega(64666) = 3.
MATHEMATICA
Select[Range[10^7], DivisorSigma[{0, 1}, #] == DivisorSigma[{0, 1}, # + 1] && PrimeNu[#] != PrimeNu[# + 1] &] (* Amiram Eldar, Jan 20 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin P. Thompson, Jan 16 2022
STATUS
approved