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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.
7
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.
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.
Not a subsequence of A342006.
Sequence in context: A044833 A033005 A072066 * A369035 A055065 A181311
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 04 2021
EXTENSIONS
Name changed by Antti Karttunen, Mar 12 2021
STATUS
approved