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%I #12 Feb 07 2023 05:56:57
%S 2,4,6,10,16,20,28,31,39,48,51,65,71,75,84,94,107,110,120,129,133,145,
%T 152,163,180,187,191,199,202,212,238,246,258,261,282,286,297,309,319,
%U 330,342,344,366,372,377,382,407,431,440,443,450,463,468,487,498
%N a(n) is the index m such that A001694(m) = prime(n)^2.
%H Reinhard Zumkeller, <a href="/A258599/b258599.txt">Table of n, a(n) for n = 1..1000</a>
%F A001694(a(n)) = A001248(n) = prime(n)^2.
%F A001694(m) mod prime(n) > 0 for m < a(n).
%F Also smallest number m such that A258567(m) = prime(n):
%F A258567(a(n)) = A000040(n) and A258567(m) != A000040(n) for m < a(n).
%e . n | p | a(n) | A001694(a(n)) = A001248(n) = p^2
%e . ----+----+-------+---------------------------------
%e . 1 | 2 | 2 | 4
%e . 2 | 3 | 4 | 9
%e . 3 | 5 | 6 | 25
%e . 4 | 7 | 10 | 49
%e . 5 | 11 | 16 | 121
%e . 6 | 13 | 20 | 169
%e . 7 | 17 | 28 | 289
%e . 8 | 19 | 31 | 361
%e . 9 | 23 | 39 | 529
%e . 10 | 29 | 48 | 841
%e . 11 | 31 | 51 | 961
%e . 12 | 37 | 65 | 1369
%e . 13 | 41 | 71 | 1681
%e . 14 | 43 | 75 | 1849
%e . 15 | 47 | 84 | 2209
%e . 16 | 53 | 94 | 2809
%e . 17 | 59 | 107 | 3481
%e . 18 | 61 | 110 | 3721
%e . 19 | 67 | 120 | 4489
%e . 20 | 71 | 129 | 5041
%e . 21 | 73 | 133 | 5329
%e . 22 | 79 | 145 | 6241
%e . 23 | 83 | 152 | 6889
%e . 24 | 89 | 163 | 7921
%e . 25 | 97 | 180 | 9409 .
%t With[{m = 60}, c = Select[Range[Prime[m]^2], Min[FactorInteger[#][[;; , 2]]] > 1 &]; 1 + Flatten[FirstPosition[c, #] & /@ (Prime[Range[m]]^2)]] (* _Amiram Eldar_, Feb 07 2023 *)
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a258599 = (+ 1) . fromJust . (`elemIndex` a258567_list) . a000040
%Y Cf. A258567, A000040, A001248, A001694, A258600, A258601, A258602, A258603.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 06 2015
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