# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a357310 Showing 1-1 of 1 %I A357310 #14 Jan 05 2024 02:51:01 %S A357310 1,1,2,1,3,4,5,1,2,6,7,3,8,9,10,1,11,4,12,5,13,14,15,2,6,16,3,7,17,18, %T A357310 19,1,20,21,22,8,23,24,25,4,26,27,28,9,10,29,30,2,11,12,31,13,32,5,33, %U A357310 6,34,35,36,14,37,38,15,1,39,40,41,16,42,43,44,7,45,46,17,18,47,48,49,3 %N A357310 a(n) is the number of j in the range 1 <= j <= n with the same maximal exponent in prime factorization as n. %H A357310 Alois P. Heinz, Table of n, a(n) for n = 1..20000 %F A357310 a(n) = |{j <= n : A051903(j) = A051903(n)}|. %F A357310 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1/zeta(2)^2 + Sum_{k>=3} (1/zeta(k+1) - 1/zeta(k))^2 = 0.43029326822775728041... . - _Amiram Eldar_, Jan 05 2024 %p A357310 f:= proc(n) option remember; `if`(n=1, 0, %p A357310 max(map(i-> i[2], ifactors(n)[2]))) %p A357310 end: %p A357310 b:= proc(n) option remember; `if`(n<1, 0, b(n-1)+x^f(n)) end: %p A357310 a:= n-> coeff(b(n), x, f(n)): %p A357310 seq(a(n), n=1..80); # _Alois P. Heinz_, Sep 23 2022 %t A357310 Table[Length[Select[Range[n], If[# == 1, 0, Max @@ Last /@ FactorInteger[#]] == If[n == 1, 0, Max @@ Last /@ FactorInteger[n]] &]], {n, 1, 80}] %t A357310 seq[max_] := Module[{e = Join[{0}, Table[Max @@ FactorInteger[n][[;; , 2]], {n, 2, max}]], c = Table[0, {max}]}, Do[c[[k]] = 1 + Count[e[[1 ;; k - 1]], e[[k]]], {k, 1, max}]; c]; seq[100] (* _Amiram Eldar_, Jan 05 2024 *) %o A357310 (PARI) lista(nmax) = {my(e = vector(nmax, k, if(k==1, 0, vecmax(factor(k)[,2]))), c); for(k = 1, nmax, c = 1; for(j = 1, k-1, c += (e[j] == e[k])); print1(c, ", "));} \\ _Amiram Eldar_, Jan 05 2024 %Y A357310 Cf. A000079 (positions of 1's), A051903, A058933, A289023. %K A357310 nonn %O A357310 1,3 %A A357310 _Ilya Gutkovskiy_, Sep 23 2022 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE