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%I #4 Jun 06 2015 17:26:47
%S 2,6,13,22,45,58,87,102,135,181,198,249,281,298,331,379,430,444,488,
%T 525,539,584,620,663,720,755,767,794,810,847,944,969,1014,1028,1099,
%U 1111,1154,1196,1225,1267,1306,1317,1384,1399,1427,1433,1516,1596,1620,1633
%N Smallest number m such that A069493(m) = prime(n)^6.
%C A069493(a(n)) = A030516(n) = prime(n)^6;
%C A069493(m) mod prime(n) > 0 for m < a(n);
%C also smallest number m such that A258571(m) = prime(n):
%C A258571(a(n)) = A000040(n) and A258571(m) != A000040(n) for m < a(n).
%H Reinhard Zumkeller, <a href="/A258603/b258603.txt">Table of n, a(n) for n = 1..1000</a>
%e . n | p | a(n) | A069493(a(n)) = A030516(n) = p^6
%e . ----+----+-------+---------------------------------
%e . 1 | 2 | 2 | 64
%e . 2 | 3 | 6 | 729
%e . 3 | 5 | 13 | 15625
%e . 4 | 7 | 22 | 117649
%e . 5 | 11 | 45 | 1771561
%e . 6 | 13 | 58 | 4826809
%e . 7 | 17 | 87 | 24137569
%e . 8 | 19 | 102 | 47045881
%e . 9 | 23 | 135 | 148035889
%e . 10 | 29 | 181 | 594823321
%e . 11 | 31 | 198 | 887503681
%e . 12 | 37 | 249 | 2565726409
%e . 13 | 41 | 281 | 4750104241
%e . 14 | 43 | 298 | 6321363049
%e . 15 | 47 | 331 | 10779215329
%e . 16 | 53 | 379 | 22164361129
%e . 17 | 59 | 430 | 42180533641
%e . 18 | 61 | 444 | 51520374361
%e . 19 | 67 | 488 | 90458382169
%e . 20 | 71 | 525 | 128100283921
%e . 21 | 73 | 539 | 151334226289
%e . 22 | 79 | 584 | 243087455521
%e . 23 | 83 | 620 | 326940373369
%e . 24 | 89 | 663 | 496981290961
%e . 25 | 97 | 720 | 832972004929 .
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a258603 = (+ 1) . fromJust . (`elemIndex` a258571_list) . a000040
%Y Cf. a258571, A000040, A030516, A069493, A258599, A258600, A258601, A258602.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 06 2015
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