

A369020


Numbers k such that k and k+1 have the same maximal exponent in their prime factorization.


3



2, 5, 6, 10, 13, 14, 21, 22, 29, 30, 33, 34, 37, 38, 41, 42, 44, 46, 49, 57, 58, 61, 65, 66, 69, 70, 73, 75, 77, 78, 80, 82, 85, 86, 93, 94, 98, 99, 101, 102, 105, 106, 109, 110, 113, 114, 116, 118, 122, 129, 130, 133, 135, 137, 138, 141, 142, 145, 147, 154, 157
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OFFSET

1,1


COMMENTS

Differs from A358817 by having the terms 99, 165, 166, ..., which are not in A358817, and not having the terms 1, 440, 1331, 1575, ..., which are in A358817.
If k is a term then k*(k+1) is a term of A362605.
The asymptotic density of this sequence is d(2) + Sum_{k>=2} (d(k) + d(k+1)  2 * d2(k)) = 0.36939178586283962461..., where d(k) = Product_{p prime} (1  2/p^k) and d2(k) = Product_{p prime} (1  1/p^k  1/p^(k1)).


LINKS



MATHEMATICA

emax[n_] := emax[n] = Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; Select[Range[200], emax[#] == emax[# + 1] &]


PROG

(PARI) emax(n) = if(n == 1, 0, vecmax(factor(n)[, 2]));
lista(kmax) = {my(e1 = 0, e2); for(k = 2, kmax, e2 = emax(k); if(e1 == e2, print1(k1, ", ")); e1 = e2); }


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



