A355542 Numbers k such that A272718(k) is divisible by k.

1, 2, 3, 11, 13, 50, 81, 96, 395, 640, 59136, 65719, 632621, 1342813, 2137073, 2755370, 3446370, 10860093, 321939569, 1872591111, 8858043355

Offset: 1

Author

Amiram Eldar, Jul 06 2022

Keywords

• nonn
• more

Comments

Numbers k such that the mean value of A018804 over the range 1..k is an integer.

The corresponding quotients are 1, 2, 3, 13, 16, 80, 141, 172, 865, 1500, 219530, 246058, 2804048, 6259092, 10263121, 13445321, 17051542, 57521176, 2036840289, 12849666590, 64967828053, ... .

a(22) > 6.5*10^10, if it exists.

Examples

			11 is a term since A061201(11) = 143 = 11 * 13 is divisible by 11.
		

Crossrefs

Cf. A018804, A272718.

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

Programs

Mathematica

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