A379923 Numbers m that divide the alternating sum Sum_{k=1..m} (-1)^k * A000005(k).

1, 5, 18, 22, 25, 29, 197, 1350, 1360, 1362, 1368, 1381, 1391, 1395, 10200, 75486, 75490, 557768, 557843, 557853, 557898, 4121846, 4122064, 4122112, 4122222, 30457732, 30457773, 30457835, 30458040, 30458133, 30458138, 30458140, 30458335, 225056911, 225056919, 225056925, 225056989

Offset: 1

Author

Amiram Eldar, Jan 06 2025

Keywords

• nonn

Comments

Numbers m such that m | A307704(m).

The corresponding quotients, A307704(m)/m, are -1, 0, 1, 1, 1, 1, 2, 3, 3, 3, ... (see the link for more values).

a(38) > 2*10^10, if it exists.

Links

• Amiram Eldar, Table of n, a(n), A307704(a(n))/a(n) for n = 1..37.

Crossrefs

Cf. A000005, A307704.

Similar sequences: A050226, A048290, A056550, A064605, A067929, A067931, A379922, A379924.

Programs

Mathematica

With[{m = 10000}, Position[Accumulate[Table[(-1)^n * DivisorSigma[0, n], {n, 1, m}]]/Range[m], _?IntegerQ] // Flatten]

PARI

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