A342018 Numbers k such that the arithmetic derivative of A276086(k) is divisible by at least one prime power divisor of the form p^p, where A276086 gives the prime product form of primorial base expansion of its argument.

8, 16, 24, 36, 44, 52, 64, 72, 80, 88, 92, 100, 108, 116, 120, 126, 128, 136, 144, 156, 164, 172, 184, 192, 200, 208, 216, 222, 224, 232, 244, 252, 260, 268, 271, 272, 280, 288, 296, 300, 308, 316, 324, 336, 344, 348, 352, 364, 372, 380, 388, 392, 397, 400, 408, 416, 424, 432, 440, 444, 448, 452, 460, 468, 476, 480, 488, 493, 496

Offset

1,1

Comments

Numbers k for which A342019(k) > 0, or equally, A342007(A327860(k)) = A342017(k) is larger than one, or equally A342007(A342002(k)) > 1, that is, k for which A342023(A342002(k)) = 1.

The first odd term is a(35) = 271.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

Example

8 is present as A276086(8) = 15, A003415(15) = 8 = 2^3, which is thus divisible by p^p (with p=2 in this case).
271 is present as A276086(271) = 1078, A003415(1078) = 945 = 3^3 * 5 * 7, which is thus divisible by p^p (with p=3 in this case).

Mathematica

Block[{b = MixedRadix[Reverse@ Prime@ Range@ 12]}, Position[#, _?(# > 1 &)][[All, 1]] &@ Array[Function[k, Times @@ Map[#1^Floor[#2/#1] & @@ # &, FactorInteger[#]] &@ If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]] ] &@ Abs[Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ k, Reverse@ k}]]@ IntegerDigits[#, b] &, 500]] (* Michael De Vlieger, Mar 12 2021 *)

Prog

(PARI) isA342018(n) = (A342017(n)>1);

Crossrefs

Positions of terms larger than one in A342017, of nonzero terms in A342019.

Cf. A003415, A276086, A327860, A342002, A342007, A342017, A342019, A342023.

Not a subsequence of A342006.

Sequence in context: A044833 A033005 A072066 * A369035 A055065 A181311

Adjacent sequences: A342015 A342016 A342017 * A342019 A342020 A342021

Keyword

nonn

Author

Antti Karttunen, Mar 04 2021

Extensions

Name changed by Antti Karttunen, Mar 12 2021

Status

approved