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%I #4 Jun 06 2015 17:26:33
%S 2,5,12,20,37,45,68,82,106,142,153,194,215,227,251,290,321,336,373,
%T 395,408,442,463,499,542,566,573,600,612,634,709,728,758,769,819,831,
%U 860,895,916,947,971,980,1034,1043,1057,1069,1131,1190,1208,1219,1240,1265
%N Smallest number m such that A069492(m) = prime(n)^5.
%C A069492(a(n)) = A050997(n) = prime(n)^5;
%C A069492(m) mod prime(n) > 0 for m < a(n);
%C also smallest number m such that A258570(m) = prime(n):
%C A258570(a(n)) = A000040(n) and A258570(m) != A000040(n) for m < a(n).
%H Reinhard Zumkeller, <a href="/A258602/b258602.txt">Table of n, a(n) for n = 1..1000</a>
%e . n | p | a(n) | A069492(a(n)) = A050997(n) = p^5
%e . ----+----+-------+---------------------------------
%e . 1 | 2 | 2 | 32
%e . 2 | 3 | 5 | 243
%e . 3 | 5 | 12 | 3125
%e . 4 | 7 | 20 | 16807
%e . 5 | 11 | 37 | 161051
%e . 6 | 13 | 45 | 371293
%e . 7 | 17 | 68 | 1419857
%e . 8 | 19 | 82 | 2476099
%e . 9 | 23 | 106 | 6436343
%e . 10 | 29 | 142 | 20511149
%e . 11 | 31 | 153 | 28629151
%e . 12 | 37 | 194 | 69343957
%e . 13 | 41 | 215 | 115856201
%e . 14 | 43 | 227 | 147008443
%e . 15 | 47 | 251 | 229345007
%e . 16 | 53 | 290 | 418195493
%e . 17 | 59 | 321 | 714924299
%e . 18 | 61 | 336 | 844596301
%e . 19 | 67 | 373 | 1350125107
%e . 20 | 71 | 395 | 1804229351
%e . 21 | 73 | 408 | 2073071593
%e . 22 | 79 | 442 | 3077056399
%e . 23 | 83 | 463 | 3939040643
%e . 24 | 89 | 499 | 5584059449
%e . 25 | 97 | 542 | 8587340257 .
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a258602 = (+ 1) . fromJust . (`elemIndex` a258570_list) . a000040
%Y Cf. a258570, A000040, A050997, A069492, A258599, A258600, A258601, A258603.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 06 2015
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