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A328252 Numbers that are not squarefree, but whose arithmetic derivative (A003415) is. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A069562 A072502 A195268 * A227279 A102042 A121282

Adjacent sequences:  A328249 A328250 A328251 * A328253 A328254 A328255

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 11 2019

STATUS

approved

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Last modified November 18 12:16 EST 2019. Contains 329261 sequences. (Running on oeis4.)