

A122140


Numbers m that divide the sum of cubes of the first m primes A098999(m).


5



1, 25, 537, 661, 5199, 113253, 240621, 5337048977, 17434578479, 34216676921, 1991831965911, 4495321247369, 22567781434431, 37328883555791, 110447613624133, 188368390470877, 324587968952249
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(9) > 6*10^9.  Donovan Johnson, Oct 15 2012
a(11) > 10^11.  Robert Price, Mar 29 2013
a(12) > 2*10^12.  Paul W. Dyson, Jan 05 2021
a(13) > 5*10^12.  Bruce Garner, Feb 28 2021
a(14) > 2.3*10^13.  Bruce Garner, Apr 06 2021
a(15) > 4*10^13.  Bruce Garner, May 13 2021
a(16) > 1.5*10^14.  Bruce Garner, Jan 08 2022
a(17) > 3.4*10^14.  Bruce Garner, Jul 31 2022


LINKS

Table of n, a(n) for n=1..17.
OEIS Wiki, Sums of powers of primes divisibility sequences.


EXAMPLE

a(2) = 25 because 25 is the first number n>1 that divides sum of cubes of the first n primes. A098999(25) mod 25 = (2^3 + 3^3 + 5^3 + ... + 89^3 + 97^3) mod 25 = 0.


MATHEMATICA

s = 0; t = {}; Do[s = s + Prime[n]^3; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 1000000}]; t


CROSSREFS

Cf. A098999.
Sequence in context: A282689 A282874 A144942 * A083191 A226299 A264378
Adjacent sequences: A122137 A122138 A122139 * A122141 A122142 A122143


KEYWORD

nonn,more


AUTHOR

Alexander Adamchuk, Aug 21 2006


EXTENSIONS

a(8) from Donovan Johnson, Oct 15 2012
a(9)a(10) from Robert Price, Mar 29 2013
a(11) from Paul W. Dyson, Jan 05 2021
a(12) from Bruce Garner, Feb 28 2021
a(13) from Bruce Garner, Apr 06 2021
a(14) from Bruce Garner, May 13 2021
a(15) from Bruce Garner, Jan 08 2022
a(16) from Paul W. Dyson, Jan 17 2022
a(17) from Bruce Garner, Jul 31 2022


STATUS

approved



