A355541 Numbers k such that A061201(k) is divisible by k.

1, 2, 7, 31, 1393, 5012, 7649, 50235, 147296, 426606, 611769, 3491681, 9324642, 11815109, 53962364, 82680301, 96789197, 230882246, 378444764, 1489280093, 1489280606, 3651325650, 5891877914, 5891877947, 5891877966, 58604540872

Offset: 1

Author

Amiram Eldar, Jul 06 2022

Keywords

• nonn
• more

Comments

Numbers k such that the mean value of A007425 over the range 1..k is an integer.

The corresponding quotients are 1, 2, 4, 9, 32, 43, 47, 67, 80, 94, 99, 125, 141, 145, 172, 180, 183, 200, 210, 239, 239, 259, 270, 270, 270, 326, ... .

a(27) > 7.5*10^10, if it exists.

Examples

			7 is a term since A061201(7) = 28 = 4 * 7 is divisible by 7.
		

Crossrefs

Cf. A007425, A061201.

Similar sequences: A045345, A050226, A056550, A064605, A064606, A064607, A064610, A064611, A064612, A048290.

Programs

Mathematica

f[p_, e_] := (e+1)*(e+2)/2;  d3[1] = 1; d3[n_] := Times @@ f @@@ FactorInteger[n]; sum = 0; seq = {}; Do[sum += d3[n]; If[Divisible[sum, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq