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

1,2

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.

Links

Table of n, a(n) for n=1..21.

Example

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

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

Crossrefs

Cf. A018804, A272718.

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

Sequence in context: A068820 A129670 A215374 * A057324 A139052 A076491

Adjacent sequences: A355539 A355540 A355541 * A355543 A355544 A355545

Keyword

nonn,more

Author

Amiram Eldar, Jul 06 2022

Status

approved