|
%I #16 Feb 07 2023 05:57:28
%S 2,4,8,13,23,29,39,45,57,75,81,99,110,117,130,149,169,176,197,209,212,
%T 236,250,270,295,309,317,328,337,354,399,414,436,445,477,483,506,529,
%U 541,563,585,591,631,635,654,657,697,747,758,765,781,803,809,845,864
%N a(n) is the index m such that A036966(m) = prime(n)^3.
%H Amiram Eldar, <a href="/A258600/b258600.txt">Table of n, a(n) for n = 1..1000</a>
%F A036966(a(n)) = A030078(n) = prime(n)^3.
%F A036966(m) mod prime(n) > 0 for m < a(n).
%F Also smallest number m such that A258568(m) = prime(n):
%F A258568(a(n)) = A000040(n) and A258568(m) != A000040(n) for m < a(n).
%e . n | p | a(n) | A036966(a(n)) = A030078(n) = p^3
%e . ----+----+-------+---------------------------------
%e . 1 | 2 | 2 | 8
%e . 2 | 3 | 4 | 27
%e . 3 | 5 | 8 | 125
%e . 4 | 7 | 13 | 343
%e . 5 | 11 | 23 | 1331
%e . 6 | 13 | 29 | 2197
%e . 7 | 17 | 39 | 4913
%e . 8 | 19 | 45 | 6859
%e . 9 | 23 | 57 | 12167
%e . 10 | 29 | 75 | 24389
%e . 11 | 31 | 81 | 29791
%e . 12 | 37 | 99 | 50653
%e . 13 | 41 | 110 | 68921
%e . 14 | 43 | 117 | 79507
%e . 15 | 47 | 130 | 103823
%e . 16 | 53 | 149 | 148877
%e . 17 | 59 | 169 | 205379
%e . 18 | 61 | 176 | 226981
%e . 19 | 67 | 197 | 300763
%e . 20 | 71 | 209 | 357911
%e . 21 | 73 | 212 | 389017
%e . 22 | 79 | 236 | 493039
%e . 23 | 83 | 250 | 571787
%e . 24 | 89 | 270 | 704969
%e . 25 | 97 | 295 | 912673 .
%t With[{m = 60}, c = Select[Range[Prime[m]^3], Min[FactorInteger[#][[;; , 2]]] > 2 &]; 1 + Flatten[FirstPosition[c, #] & /@ (Prime[Range[m]]^3)]] (* _Amiram Eldar_, Feb 07 2023 *)
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a258600 = (+ 1) . fromJust . (`elemIndex` a258568_list) . a000040
%Y Cf. A258568, A000040, A030078, A036966, A258599, A258601, A258602, A258603.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 06 2015
%E a(11)-a(55) and example corrected by _Amiram Eldar_, Feb 07 2023
| 