|
%I #6 Feb 02 2023 13:48:55
%S 2,5,10,16,28,37,55,61,80,105,112,140,160,165,183,209,236,244,265,283,
%T 289,316,335,360,389,408,414,430,435,452,505,520,542,549,589,598,613,
%U 637,651,675,697,701,737,743,754,765,806,844,866,870,880,899,908,940
%N Smallest number m such that A036967(m) = prime(n)^4.
%C A036967(a(n)) = A030514(n) = prime(n)^4;
%C A036967(m) mod prime(n) > 0 for m < a(n);
%C also smallest number m such that A258569(m) = prime(n):
%C A258569(a(n)) = A000040(n) and A258569(m) != A000040(n) for m < a(n).
%H Reinhard Zumkeller, <a href="/A258601/b258601.txt">Table of n, a(n) for n = 1..1000</a>
%e . n | p | a(n) | A036967(a(n)) = A030514(n) = p^4
%e . ----+----+-------+---------------------------------
%e . 1 | 2 | 2 | 16
%e . 2 | 3 | 5 | 81
%e . 3 | 5 | 10 | 625
%e . 4 | 7 | 16 | 2401
%e . 5 | 11 | 28 | 14641
%e . 6 | 13 | 37 | 28561
%e . 7 | 17 | 55 | 83521
%e . 8 | 19 | 61 | 130321
%e . 9 | 23 | 80 | 279841
%e . 10 | 29 | 105 | 707281
%e . 11 | 31 | 112 | 923521
%e . 12 | 37 | 140 | 1874161
%e . 13 | 41 | 160 | 2825761
%e . 14 | 43 | 165 | 3418801
%e . 15 | 47 | 183 | 4879681
%e . 16 | 53 | 209 | 7890481
%e . 17 | 59 | 236 | 12117361
%e . 18 | 61 | 244 | 13845841
%e . 19 | 67 | 265 | 20151121
%e . 20 | 71 | 283 | 25411681
%e . 21 | 73 | 289 | 28398241
%e . 22 | 79 | 316 | 38950081
%e . 23 | 83 | 335 | 47458321
%e . 24 | 89 | 360 | 62742241
%e . 25 | 97 | 389 | 88529281
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a258601 = (+ 1) . fromJust . (`elemIndex` a258569_list) . a000040
%Y Cf. A258569, A000040, A030514, A036967, A258599, A258600, A258602, A258603.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 06 2015
| 