

A309556


Composite numbers m such that m divides Sum_{k=1..m1} (lcm(1,2,...,(m1)) / k)^2.


0




OFFSET

1,1


COMMENTS

Composites m such that m  H_2(m1) * lcm(1^2,2^2,...,(m1)^2), where H_2(m) = 1/1^2 + 1/2^2 + ... + 1/m^2.
By Wolstenholme's theorem, if p > 3 is a prime, then p divides the numerator of H_2(p1) and thus H_2(p1) * lcm(1,2^2,...,(p1)^2) == 0 (mod p). This sequence is formed by the pseudoprimes that are solutions of this congruence.
a(5) > 10^7 if it exists.


LINKS

Table of n, a(n) for n=1..4.
Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.
Wikipedia, Wolstenholme's theorem.


MATHEMATICA

s = 0; c = 1; n = 1; seq = {}; Do[s += 1/n^2; c = LCM[c, n^2]; n++; If[CompositeQ[n] && Divisible[s*c, n], AppendTo[seq, n]], {2 * 10^6}]; seq


CROSSREFS

Cf. A007406, A007407, A025529 (see our comment), A051418.
Sequence in context: A185530 A057851 A058326 * A206092 A233965 A157758
Adjacent sequences: A309553 A309554 A309555 * A309557 A309558 A309559


KEYWORD

nonn,bref,more


AUTHOR

Amiram Eldar and Thomas Ordowski, Aug 07 2019


STATUS

approved



