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%I #19 Feb 25 2024 13:11:58
%S 1,3,2,6,5,4,10,23,12,7,39,9,97,24,164,484,2759,5044,109,32334,114605,
%T 216960,8,14,252,785135,5503557,28,39222428,75703838,548300521,1496,
%U 2063337476,4008153424,29523940595,3858,112174606866,834662735468,11
%N a(n) is such that A145521(n) = A053810(a(n)).
%C This sequence is a permutation of the positive integers. It is its own inverse permutation.
%F a(n) = Sum_{primes p, 2^p <= A145521(n)} A000720(floor(A145521(n)^(1/p))).
%F Also, if A145521(n) = 2^k then a(n) = A060967(k) + Sum_{primes p, 3 <= p <= k} A000720(floor(2^(k/p))). - _Jason Yuen_, Jan 31 2024
%e The primes raised to prime exponents form the sequence, when the terms are arranged in numerical order, 4,8,9,25,27,32,49,121,125,128,...(sequence A053810). The 10th term is 128, which is 2^7. So the 10th term of sequence A145521 is 7^2 = 49. 49 is the 7th term of A053810. So a(10) = 7 and a(7) = 10.
%o (PARI) lista(nn) = {my(c, m); for(k=1, nn, if(isprime(isprimepower(k, &p)), c=0; m=bigomega(k)^p; forprime(q=2, sqrtint(m), c+=primepi(logint(m, q))); print1(c, ", "))); } \\ _Jinyuan Wang_, Feb 25 2020
%o (Python)
%o from itertools import count
%o from sympy import integer_nthroot, isprime, primepi
%o def A145522(n):
%o total = 0
%o for p in count(2):
%o if 2**p > A145521(n): break
%o if isprime(p): total += primepi(integer_nthroot(A145521(n), p)[0])
%o return total # _Jason Yuen_, Jan 31 2024
%Y Cf. A053810, A145521, A000720, A060967.
%K nonn,more
%O 1,2
%A _Leroy Quet_, Oct 12 2008
%E a(11)-a(28) from _Ray Chandler_, Nov 01 2008
%E a(29)-a(32) from _Jinyuan Wang_, Feb 25 2020
%E a(33)-a(39) from _Jason Yuen_, Jan 31 2024
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