

A328305


Numbers that are cubefree, but not squarefree and whose first arithmetic derivative is not squarefree, but some kth (with k >= 2) derivative is.


6



50, 99, 207, 306, 531, 549, 725, 747, 819, 931, 1083, 1175, 1611, 1775, 1899, 2057, 2075, 2299, 2331, 2367, 2499, 2525, 2842, 2853, 2891, 3425, 3577, 3610, 3771, 3789, 3843, 4059, 4149, 4311, 4475, 4575, 4626, 4693, 4775, 4998, 5239, 5274, 5341, 5547, 5634, 5706, 5715, 5746, 5819, 5949, 6147, 6223, 6275, 6381, 6413, 6475, 6575
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OFFSET

1,1


COMMENTS

Numbers n for which A051903(n) = 2 and A328248(n) > 2.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


EXAMPLE

50 is not squarefree, as 50 = 2 * 5^2, and neither its arithmetic derivative A003415(50) = 45 = 3^2 * 5 is squarefree, but its second derivative A003415(45) = 39 = 3*13 is, thus 50 is included in this sequence.


PROG

(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));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328248(n) = { my(k=1); while(n && !issquarefree(n), k++; n = A003415checked(n)); (!!n*k); };
isA067259(n) = (2==A051903(n));
isA328305(n) = (isA067259(n)&&(A328248(n)>2));


CROSSREFS

Cf A003415, A051903, A328248, A328253.
Subsequence of A067259, A328303, A328304 and A328321.
Sequence in context: A044139 A044520 A158066 * A304840 A043220 A039397
Adjacent sequences: A328302 A328303 A328304 * A328306 A328307 A328308


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 13 2019


STATUS

approved



