# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a377794 Showing 1-1 of 1 %I A377794 #7 Nov 13 2024 17:17:56 %S A377794 2,2,3,3,5,5,6,6,7,8,8,9,10,10,10,11,12,12,13,13,12,13,13,14,15,15,15, %T A377794 15,14,14,17,17,18,17,19,18,19,19,19,20,20,20,21,21,20,20,22,23,23,23, %U A377794 23,23,22,23,24,24,24,24,24,24,23,24,26,26,26,25,27,28,29 %N A377794 a(n) is the greatest number of prime factors with multiplicity of squarefree composite k such that k has lpf(k) = prime(n) such that m <= a(n), where lpf = A020639, m = floor(log k / log lpf(k)). %C A377794 The smallest k such that lpf(k) = prime(n) with Omega(k) = A001222(k) = a(n) is the product of prime(n..n+a(n)-1). %H A377794 Michael De Vlieger, Table of n, a(n) for n = 1..10000 %H A377794 Michael De Vlieger, Log log scatterplot of a(n), n = 1..16384. %e A377794 Table relating the first 12 terms with prime decomposition of smallest k in A377713 (or A377792) such that lpf(k) = prime(n) and Omega(k) = a(n): %e A377794 n k prime factors of k a(n) %e A377794 ----------------------------------------------------------------------- %e A377794 1 6 2 * 3 2 %e A377794 2 15 3 * 5 2 %e A377794 3 385 5 * 7 * 11 3 %e A377794 4 1001 7 * 11 * 13 3 %e A377794 5 1062347 11 * 13 * 17 * 19 * 23 5 %e A377794 6 2800733 13 * 17 * 19 * 23 * 29 5 %e A377794 7 247110827 17 * 19 * 23 * 29 * 31 * 37 6 %e A377794 8 595973171 19 * 23 * 29 * 31 * 37 * 41 6 %e A377794 9 63392725189 23 * 29 * 31 * 37 * 41 * 43 * 47 7 %e A377794 10 8618654420261 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 8 %e A377794 11 18128893780549 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 8 %e A377794 12 2781907990776503 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 9 %t A377794 Table[j = 1; While[Times @@ Prime[Range[i + 1, i + j]] < Prime[i]^(j + 1), j++]; j, {i, 120}] %Y A377794 Cf. A001222, A020639, A120944, A377713, A377792. %K A377794 nonn,easy,new %O A377794 1,1 %A A377794 _Michael De Vlieger_, Nov 07 2024 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE