A324593
a(n) is the smallest number k such that n consecutive integers starting at k have the same number of odd divisors (A001227).
Original entry on oeis.org
1, 1, 5, 10, 10, 515, 2314, 2314, 1536863, 4053992, 4053992, 18584686, 146237365, 163039279, 4775943486, 13147233734, 86153130379
Offset: 1
515 has 4 odd divisors {1, 5, 103, 515}, 516 has 4 odd divisors {1, 3, 43, 129}, 517 has 4 odd divisors {1, 11, 47, 517}, 518 has 4 odd divisors {1, 7, 37, 259}, 519 has 4 odd divisors {1, 3, 173, 519} and 520 has 4 odd divisors {1, 5, 13, 65}. These the first 6 consecutive numbers with the same number of odd divisors, so a(6) = 515.
A324594
a(n) is the smallest number k such that n consecutive integers starting at k have the same number of nonprime divisors (A033273).
Original entry on oeis.org
1, 1, 1, 19940, 204323, 294590, 310042685, 2587701932494, 2587701932494
Offset: 1
19940 has 9 nonprime divisors {1, 4, 10, 20, 1994, 3988, 4985, 9970, 19940}, 19941 has 9 nonprime divisors {1, 51, 69, 289, 391, 867, 1173, 6647, 19941}, 19942 has 9 nonprime divisors {1, 26, 118, 169, 338, 767, 1534, 9971, 19942} and 19943 has 9 nonprime divisors {1, 49, 77, 259, 407, 539, 1813, 2849, 19943}. These the first 4 consecutive numbers with the same number of nonprime divisors, so a(4) = 19940.
A369022
a(n) is the least start of a run of exactly n consecutive integers with the same maximal exponent in their prime factorization, or -1 if no such run exists.
Original entry on oeis.org
1, 2, 5, 844, 30923, 671346, 8870025
Offset: 1
-
emax[n_] := Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; ind = Position[Differences[Table[emax[n], {n, 1, 10^6}]], _?(# != 0 &)] // Flatten; d = Differences[ind]; seq = {1}; Do[i = FirstPosition[d, k]; If[MissingQ[i], Break[]]; AppendTo[seq, ind[[i[[1]]]] + 1], {k, 2, Max[d]}]; seq
-
emax(n) = vecmax(factor(n)[, 2]);
lista(len) = {my(v = vector(len), w = [0], m, c = 0, k = 2); while(c < len, e = emax(k); m = #w; if(e == w[m], w = concat(w, e), if(m < = len && v[m] == 0, v[m] = k-m; c++); w = [e]); k++); v;}
Showing 1-3 of 3 results.
Comments