login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A328303 Numbers whose arithmetic derivative is not squarefree. 6
0, 1, 4, 8, 12, 14, 15, 16, 20, 24, 27, 28, 32, 35, 36, 39, 40, 44, 46, 48, 50, 51, 52, 54, 55, 56, 60, 64, 65, 68, 72, 76, 77, 80, 81, 84, 86, 87, 88, 91, 92, 94, 95, 96, 99, 100, 104, 108, 111, 112, 115, 116, 119, 120, 122, 123, 124, 125, 128, 132, 135, 136, 138, 140, 141, 143, 144, 146, 148, 152, 155, 156, 158, 159, 160, 162, 164, 168, 172, 176, 180, 183, 184, 187, 188, 189, 192, 194, 196, 200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers n for which either A003415(n) = 0 or A051903(A003415(n)) > 1.

LINKS

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

EXAMPLE

Arithmetic derivative of 1 is A003415(1) = 0, which is not a squarefree number (not in A005117), thus 1 is included in this sequence. Ditto for 0, as A003415(0) = 0.

Arithmetic derivative of 8 is A003415(8) = 12 = 2^2 * 3, which is not squarefree, thus 8 is included in this sequence.

Arithmetic derivative of 15 is A003415(15) = 8 = 2^3, which is not squarefree, thus 15 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]));

isA328303(n) = !issquarefree(A003415(n));

CROSSREFS

Cf. A003415, A005177, A008966, A051903.

Complement of the union of A000040 and A328234.

Cf. A328245, A328251, A328253, A328304, A328305 (subsequences).

Sequence in context: A101887 A320498 A311078 * A311079 A257221 A092453

Adjacent sequences:  A328300 A328301 A328302 * A328304 A328305 A328306

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 13 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 06:34 EST 2019. Contains 329784 sequences. (Running on oeis4.)