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 A342028 Numbers k such that k and k+1 both have mutually distinct exponents in their prime factorization (A130091). 5
 1, 2, 3, 4, 7, 8, 11, 12, 16, 17, 18, 19, 23, 24, 27, 28, 31, 40, 43, 44, 47, 48, 49, 52, 53, 63, 67, 71, 72, 75, 79, 80, 88, 96, 97, 98, 103, 107, 108, 112, 116, 124, 127, 135, 136, 147, 148, 151, 152, 162, 163, 171, 172, 175, 188, 191, 192, 199, 207, 211, 223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Kevser Aktaş and M. Ram Murty, On the number of special numbers, Proceedings - Mathematical Sciences, Vol. 127, No. 3 (2017), pp. 423-430; alternative link. Bernardo Recamán Santos, Consecutive numbers with mutually distinct exponents in their canonical prime factorization, MathOverflow, Mar 30 2015. EXAMPLE 2 is a term since both 2 and 3 have a single exponent (1) in their prime factorization. 5 is not a term since 6 = 2*3 has two equal exponents (1) in its prime factorization. MATHEMATICA q[n_] := Length[(e = FactorInteger[n][[;; , 2]])] == Length[Union[e]]; Select[Range[250], q[#] && q[# + 1] &] CROSSREFS Subsequence of A130091. Subsequences: A342029, A342030, A342031. Sequence in context: A188190 A026808 A240767 * A284937 A271441 A328421 Adjacent sequences:  A342025 A342026 A342027 * A342029 A342030 A342031 KEYWORD nonn AUTHOR Amiram Eldar, Feb 25 2021 STATUS approved

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Last modified January 21 14:21 EST 2022. Contains 350479 sequences. (Running on oeis4.)