A379922 Numbers m that divide the alternating sum Sum_{k=1..m} (-1)^(k+1) * sigma_2(k).

1, 2, 3, 42, 329, 633, 1039, 5689, 26621, 39245, 1101875, 1216075, 40088584, 67244920, 104332211, 549673265, 777631064, 19879301756

Offset

1,2

Comments

Numbers m such that m | A379921(m).

The corresponding quotients, A379921(m)/m, are -1, 2, -2, 120, 5228, ... (see the link for more values).

a(19) > 5*10^10, if it exists.

Links

Table of n, a(n) for n=1..18.

Amiram Eldar, Table of n, a(n), A379921(a(n))/a(n) for n = 1..18.

Mathematica

With[{m = 40000}, Position[Accumulate[Table[(-1)^n * DivisorSigma[2, n], {n, 1, m}]]/Range[m], _?IntegerQ] // Flatten]

Prog

(PARI) list(lim) = my(s = 0); for(k = 1, lim, s += (-1)^k * sigma(k, 2); if(!(s % k), print1(k, ", ")));

Crossrefs

Cf. A001157 (sigma_2), A379921.

Similar sequences: A050226, A048290, A056550, A064605, A067929, A067931, A379923, A379924.

Sequence in context: A271331 A101821 A121475 * A334533 A196874 A087571

Adjacent sequences: A379919 A379920 A379921 * A379923 A379924 A379925

Keyword

nonn,more

Author

Amiram Eldar, Jan 06 2025

Status

approved