A328252 Numbers that are not squarefree, but whose arithmetic derivative (A003415) is.

9, 18, 25, 45, 49, 63, 75, 90, 98, 117, 121, 126, 147, 150, 153, 169, 171, 175, 198, 234, 242, 245, 261, 279, 289, 294, 315, 325, 333, 338, 342, 350, 361, 363, 369, 387, 414, 423, 425, 450, 475, 477, 490, 495, 507, 522, 529, 539, 550, 558, 575, 578, 603, 605, 630, 637, 639, 650, 657, 666, 711, 722, 726, 735, 738, 774, 775, 801

Offset

1,1

Links

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

Example

18 = 2 * 3^2 is not squarefree, but its arithmetic derivative A003415(18) = 21 = 3*7 is, thus 18 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]));
isA328252(n) = (!issquarefree(n) && issquarefree(A003415(n)));
(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); };
isA328252(n) = (2==A328248(n));

Crossrefs

Cf. A003415, A328253.

Row 3 of array A328250. Positions of 2's in A328248.

Setwise difference A328234 \ A005117. Intersection of A013929 and A328234.

Sequence in context: A072502 A195268 A371083 * A227279 A102042 A332551

Adjacent sequences: A328249 A328250 A328251 * A328253 A328254 A328255

Keyword

nonn

Author

Antti Karttunen, Oct 11 2019

Status

approved