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A053812 Exponents occurring in A053810.

%I A053812 #20 Aug 14 2024 01:51:17
%S A053812 2,3,2,2,3,5,2,2,3,7,2,5,2,3,2,2,2,2,3,2,2,2,11,7,3,2,2,5,2,2,2,3,2,2,
%T A053812 2,3,2,2,13,2,2,2,2,2,3,2,2,5,2,2,2,2,2,3,2,2,2,3,2,2,2,2,2,2,2,2,2,3,
%U A053812 2,2,2,2,2,2,2,3,2,2,2,2,7,2,3,2,2,2,2,2,2,3,2,2,2,2,2,2,17,2,2,2,2,3,2,2,2
%N A053812 Exponents occurring in A053810.
%H A053812 Amiram Eldar, <a href="/A053812/b053812.txt">Table of n, a(n) for n = 1..10000</a>
%F A053812 a(n) = A001222(A053810(n)). - _David Wasserman_, Feb 17 2006
%F A053812 a(n) = log(A053810(n))/log(A053811(n)). - _Amiram Eldar_, Nov 21 2020
%o A053812 (PARI) LIM = prime(80)^2; v = vector(400); count = 0; forprime (p = 2, prime(80), x = 2; while (p^x <= LIM, count++; v[count] = p^x; x = nextprime(x + 1))); v = vecsort(vector(count, i, v[i])); vector(count, i, bigomega(v[i])) \\ _David Wasserman_, Feb 17 2006
%o A053812 (Python)
%o A053812 from sympy import primepi, integer_nthroot, primerange, factorint
%o A053812 def A053812(n):
%o A053812     def f(x): return int(n-1+x-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(x.bit_length())))
%o A053812     kmin, kmax = 1,2
%o A053812     while f(kmax) >= kmax:
%o A053812         kmax <<= 1
%o A053812     while True:
%o A053812         kmid = kmax+kmin>>1
%o A053812         if f(kmid) < kmid:
%o A053812             kmax = kmid
%o A053812         else:
%o A053812             kmin = kmid
%o A053812         if kmax-kmin <= 1:
%o A053812             break
%o A053812     return list(factorint(kmax).values())[0] # _Chai Wah Wu_, Aug 13 2024
%Y A053812 Cf. A000961, A000961, A001222, A025473, A053810, A053811.
%K A053812 nonn
%O A053812 1,1
%A A053812 _Henry Bottomley_, Mar 28 2000
%E A053812 More terms from _David Wasserman_, Feb 17 2006
%E A053812 Offset corrected by _Amiram Eldar_, Nov 21 2020