A378689 a(n) = product of divisors d of n that are not coreful.
1, 1, 1, 1, 1, 6, 1, 1, 1, 10, 1, 24, 1, 14, 15, 1, 1, 54, 1, 40, 21, 22, 1, 192, 1, 26, 1, 56, 1, 27000, 1, 1, 33, 34, 35, 216, 1, 38, 39, 320, 1, 74088, 1, 88, 135, 46, 1, 3072, 1, 250, 51, 104, 1, 1458, 55, 448, 57, 58, 1, 25920000, 1, 62, 189, 1, 65, 287496
Offset: 1
Examples
Table of n, a(n), and divisors that are not coreful that produce a(n) for select n: n a(n) ----------------------------- 1 1 (empty product) 2 1 = 1 3 1 = 1 4 1 = 1 5 1 = 1 6 6 = 1*2*3 10 10 = 1*2*5 12 24 = 1*2*3*4 14 14 = 1*2*7 15 15 = 1*3*5 18 54 = 1*2*3*9 20 40 = 1*2*4*5 21 21 = 1*3*7 22 22 = 1*2*11 24 192 = 1*2*3*4*8 30 27000 = 1*2*3*5*6*10*15 36 216 = 1*2*3*4*9
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Log log scatterplot of log_10(a(n)) for n = 1..2^20.
- Michael De Vlieger, Log log scatterplot of log_10(a(n)) for n = 1..2^16 (ignoring a(n) = 1, i.e., n that is a power of a prime), showing a(n) such that n is in A286708 in purple, n in A332785 in blue, n in A120944 in green, highlighting n in A002110 in large green points.
Programs
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Mathematica
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; Table[r = rad[n]; Times @@ Select[Divisors[n], rad[#] != r &], {n, 120}] -
PARI
rad(n) = factorback(factorint(n)[, 1]); \\ A007947 a(n) = my(d=divisors(n), c=rad(n), p=1); for (i=1, #d~, if (rad(d[i]) != c, p *= d[i])); p; \\ Michel Marcus, Feb 07 2025