login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A248135 Composite numbers c that divide the sum of remainders of c' mod k, for k from 1 to c', where c' is the arithmetic derivative of c. 0
1, 12, 52, 840, 988, 1461, 4926, 21376, 130484, 210840, 297158 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

Arithmetic derivative of 12 is 16.

16 == 0 mod 1; 16 == 0 mod 2; 16 == 1 mod 3; 16 == 0 mod 4;

16 == 1 mod 5; 16 == 4 mod 6; 16 == 2 mod 7; 16 == 0 mod 8;

16 == 7 mod 9; 16 == 6 mod 10; 16 == 5 mod 11; 16 == 4 mod 12;

16 == 3 mod 13; 16 == 2 mod 14; 16 == 1 mod 15; 16 == 0 mod 16

and 0 + 0 + 1 + 0 + 1 + 4 + 2 + 0 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 36.

Finally 36 == 0 mod 12.

MAPLE

isA248135 := proc(n)

    local adir ;

    if isprime(n) then

        false;

    else

        adir := A003415(n) ;

        if modp(add(adir mod k, k=1..adir), n) = 0 then

            true;

        else

            false;

        end if;

    end if;

end proc:

for n from 1 do

    if isA248135(n) then

        print(n) ;

    end if;

end do: # R. J. Mathar, Oct 10 2014

PROG

(Python)

from sympy import isprime, factorint

A248135_list = []

for n in range(1, 10**6):

....if not isprime(n):

........a = sum([int(n*e/p) for p, e in factorint(n).items()]) if n > 1 else 0

........if not sum(a % i for i in range(1, a)) % n:

............A248135_list.append(n)

# Chai Wah Wu, Oct 19 2014

CROSSREFS

Cf. A003415.

Sequence in context: A297757 A223249 A195544 * A307916 A280660 A268186

Adjacent sequences:  A248132 A248133 A248134 * A248136 A248137 A248138

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Oct 10 2014

EXTENSIONS

a(9)-a(11) from Chai Wah Wu, Oct 19 2014

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 October 26 20:42 EDT 2021. Contains 348269 sequences. (Running on oeis4.)