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A328253 Nonsquarefree numbers whose first arithmetic derivative (A003415) is not squarefree, but the second derivative (A068346) is. 8
50, 99, 125, 207, 343, 375, 531, 686, 725, 747, 750, 819, 875, 931, 1083, 1175, 1331, 1375, 1750, 1775, 1899, 2057, 2058, 2075, 2197, 2250, 2299, 2331, 2367, 2499, 2525, 2625, 2750, 2853, 3250, 3425, 3430, 3577, 3610, 3771, 3789, 3843, 3875, 4059, 4149, 4250, 4311, 4394, 4459, 4475, 4626, 4693, 4750, 4775, 4875, 4913, 4998, 5145 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
50 (= 2 * 5^2) is not squarefree, and its first derivative A003415(50) = 45 = 3^2 * 5 also is not squarefree, but taking derivative yet again, gives A003415(45) = 39 = 3*13, which is squarefree, thus 50 is included in this sequence.
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA328253(n) = if(issquarefree(n), 0, my(u=A003415(n)); if(issquarefree(u), 0, issquarefree(A003415(u))));
(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A328248(n) = { my(k=1); while(n && !issquarefree(n), k++; n = A003415checked(n)); (!!n*k); };
isA328253(n) = (3==A328248(n));
CROSSREFS
Row 4 of array A328250. Indices of 3's in A328248.
Setwise difference A328245 \ A005117. Intersection of A013929 and A328245.
Sequence in context: A090997 A141757 A248023 * A044139 A044520 A158066
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 11 2019
STATUS
approved

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Last modified June 19 12:43 EDT 2024. Contains 373503 sequences. (Running on oeis4.)