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A360529
a(n) is the smallest k > A024619(n) such that rad(k) = rad(A024619(n)), where rad(n) = A007947(n).
2
12, 20, 18, 28, 45, 24, 40, 63, 44, 36, 52, 56, 60, 99, 68, 175, 48, 76, 117, 50, 84, 88, 75, 92, 54, 80, 153, 104, 72, 275, 98, 171, 116, 90, 124, 147, 325, 132, 136, 207, 140, 96, 148, 135, 152, 539, 156, 100, 164, 126, 425, 172, 261, 176, 120, 637, 184, 279, 188, 475, 108, 112, 297, 160, 204, 208
OFFSET
1,1
COMMENTS
Permutation of A126706.
Let m = A024619(n) and let R_m be the sequence of numbers k such that rad(k) = rad(m). a(n) gives the successor to m in R_m.
LINKS
Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16.
FORMULA
a(n) = A065642 \ A001597.
Squarefree m implies a(n) = lpf(m)*m = A020639(m)*m.
EXAMPLE
A024619(1) = 6; the smallest k > 6 such that rad(k) = 6 is a(1) = 12.
A024619(2) = 10; the smallest k > 10 such that rad(k) = 10 is a(2) = 20.
A024619(3) = 12; the smallest k > 12 such that rad(k) = rad(12) = 6 is a(3) = 18.
MATHEMATICA
rad[x_] := rad[x] = Times@ FactorInteger[x][[All, 1]]; Table[k = m + 1; Function[r, If[SquareFreeQ[m], m*FactorInteger[m][[1, 1]], While[rad[k] != r, k++]; k]][rad[m]], {m, Select[Range[2, 104], ! PrimePowerQ[#] &]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, May 01 2023
STATUS
approved