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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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000005, A000203, A001221, A054004. Sequence in context: A236469 A203712 A061738 * A342327 A198779 A104939 Adjacent sequences:  A350797 A350798 A350799 * A350801 A350802 A350803 KEYWORD nonn AUTHOR Kevin P. Thompson, Jan 16 2022 STATUS approved

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Last modified August 19 23:59 EDT 2022. Contains 356231 sequences. (Running on oeis4.)