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A258601 a(n) is the index m such that A036967(m) = prime(n)^4.

%I A258601 #20 Sep 11 2024 00:33:18
%S A258601 2,5,10,16,28,37,55,61,80,105,113,142,163,170,190,219,249,260,286,310,
%T A258601 318,352,374,407,448,472,482,505,511,536,614,634,672,682,740,754,783,
%U A258601 821,842,878,916,924,984,996,1015,1032,1103,1171,1201,1213,1233,1270,1286,1343,1379
%N A258601 a(n) is the index m such that A036967(m) = prime(n)^4.
%C A258601 A036967(a(n)) = A030514(n) = prime(n)^4;
%C A258601 A036967(m) mod prime(n) > 0 for m < a(n);
%C A258601 also smallest number m such that A258569(m) = prime(n):
%C A258601 A258569(a(n)) = A000040(n) and A258569(m) != A000040(n) for m < a(n).
%H A258601 Andrew Howroyd, <a href="/A258601/b258601.txt">Table of n, a(n) for n = 1..1000</a>
%e A258601 .   n |  p |  a(n) | A036967(a(n)) = A030514(n) = p^4
%e A258601 . ----+----+-------+---------------------------------
%e A258601 .   1 |  2 |     2 |            16
%e A258601 .   2 |  3 |     5 |            81
%e A258601 .   3 |  5 |    10 |           625
%e A258601 .   4 |  7 |    16 |          2401
%e A258601 .   5 | 11 |    28 |         14641
%e A258601 .   6 | 13 |    37 |         28561
%e A258601 .   7 | 17 |    55 |         83521
%e A258601 .   8 | 19 |    61 |        130321
%e A258601 .   9 | 23 |    80 |        279841
%e A258601 .  10 | 29 |   105 |        707281
%e A258601 .  11 | 31 |   113 |        923521
%e A258601 .  12 | 37 |   142 |       1874161
%e A258601 .  13 | 41 |   163 |       2825761
%e A258601 .  14 | 43 |   170 |       3418801
%e A258601 .  15 | 47 |   190 |       4879681
%e A258601 .  16 | 53 |   219 |       7890481
%e A258601 .  17 | 59 |   249 |      12117361
%e A258601 .  18 | 61 |   260 |      13845841
%e A258601 .  19 | 67 |   286 |      20151121
%e A258601 .  20 | 71 |   310 |      25411681
%e A258601 .  21 | 73 |   318 |      28398241
%e A258601 .  22 | 79 |   352 |      38950081
%e A258601 .  23 | 83 |   374 |      47458321
%e A258601 .  24 | 89 |   407 |      62742241
%e A258601 .  25 | 97 |   448 |      88529281
%o A258601 (Haskell)
%o A258601 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A258601 a258601 = (+ 1) . fromJust . (`elemIndex` a258569_list) . a000040
%o A258601 (Python)
%o A258601 from math import gcd
%o A258601 from sympy import prime, integer_nthroot, factorint
%o A258601 def A258601(n):
%o A258601     c, m = 0, prime(n)**4
%o A258601     for u in range(1,integer_nthroot(m,7)[0]+1):
%o A258601         if all(d<=1 for d in factorint(u).values()):
%o A258601             for w in range(1,integer_nthroot(a:=m//u**7,6)[0]+1):
%o A258601                 if gcd(w,u)==1 and all(d<=1 for d in factorint(w).values()):
%o A258601                     for y in range(1,integer_nthroot(z:=a//w**6,5)[0]+1):
%o A258601                         if gcd(w,y)==1 and gcd(u,y)==1 and all(d<=1 for d in factorint(y).values()):
%o A258601                             c += integer_nthroot(z//y**5,4)[0]
%o A258601     return c # _Chai Wah Wu_, Sep 10 2024
%o A258601 (PARI) \\ Gen(limit,k) defined in A036967.
%o A258601 a(n)=#Gen(prime(n)^4,4) \\ _Andrew Howroyd_, Sep 10 2024
%Y A258601 Cf. A258569, A000040, A030514, A036967, A258599, A258600, A258602, A258603.
%K A258601 nonn
%O A258601 1,1
%A A258601 _Reinhard Zumkeller_, Jun 06 2015
%E A258601 a(11) onwards corrected by _Chai Wah Wu_ and _Andrew Howroyd_, Sep 10 2024