A379753 Numbers that set records in A379752.
60, 120, 240, 480, 840, 1260, 1680, 2520, 3360, 5040, 7560, 10080, 15120, 20160, 27720, 36960, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 443520, 498960, 554400, 665280, 720720, 997920, 1081080, 1330560, 1441440, 2162160, 2882880, 3603600, 4324320, 5765760
Offset: 1
Keywords
Examples
Let b(n) = A379752(n). Table showing exponents of prime power factors of a(n) for n = 1..12. Example: a(6) = 1260 = 2^2 * 3^2 * 5 * 7, hence we write "2.2.1.1". n a(n) Exp. b(a(n)) ---------------------------------- 1 60 ** 2.1.1 1 6*10 2 120 ** 3.1.1 2 6*20 = 10*12 3 240 * 4.1.1 3 6*40 = 10*24 = 12*20 4 480 5.1.1 4 6*80 = 10*48 = 12*40 = 20*24 5 840 * 3.1.1.1 6 6*140 = 10*84 = 12*70 = 14*60 = 20*42 = 28*30 6 1260 * 2.2.1.1 7 7 1680 * 4.1.1.1 9 8 2520 ** 3.2.1.1 11 9 3360 5.1.1.1 12 10 5040 ** 4.2.1.1 15 11 7560 * 3.3.1.1 16 12 10080 * 5.2.1.1 19 * = a(n) is highly composite (in A002182), ** = a(n) is superior highly composite (in both A002182 and A002201).
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..226
- Michael De Vlieger, Prime Power Decomposition of a(n) for n = 1..226, expanding on the table in the example.
- Michael De Vlieger, Plot S(n) = P(omega(n))*m at (x,y) = (m, omega(n)), where S is the union of A002182 and this sequence, P is A002110, omega is A001221, and only select m that harbor S(n) shown. Shows the coincidence of many terms in this sequence with A002182. Blue represents m in A002182, gold m in both A002182 and this sequence; dark blue represents m in A002201 (and also in A002182), orange m in both A002201 and this sequence; red indicates terms in this sequence that are not in A002182. Green highlights terms in A002182 but are not determined to be in this sequence.
Programs
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Mathematica
(* Load function f at A025487 *) r = 0; s = Select[Union@ Flatten@ f[14][[4 ;; -1]], Not@*SquareFreeQ]; nn = Length[s]; Print[nn]; Reap[Do[k = s[[i]]; If[# > r, r = #; Sow[k]] &@ Count[Transpose@ {#, k/#} &@ #[[2 ;; Ceiling[Length[#]/2] ]] &@ Divisors[k], _?(And[1 < GCD @@ {##}, Nor[Divisible[#2, rad[#1]], Divisible[#1, rad[#2]] ] ] & @@ # &)], {i, nn}] ][[-1, 1]]
Comments