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 A145522 a(n) is such that A145521(n) = A053810(a(n)). 2
 1, 3, 2, 6, 5, 4, 10, 23, 12, 7, 39, 9, 97, 24, 164, 484, 2759, 5044, 109, 32334, 114605, 216960, 8, 14, 252, 785135, 5503557, 28, 39222428, 75703838, 548300521, 1496, 2063337476, 4008153424, 29523940595, 3858, 112174606866, 834662735468, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is a permutation of the positive integers. It is its own inverse permutation. LINKS Table of n, a(n) for n=1..39. FORMULA a(n) = Sum_{primes p, 2^p <= A145521(n)} A000720(floor(A145521(n)^(1/p))). 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 EXAMPLE 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. PROG (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 (Python) from itertools import count from sympy import integer_nthroot, isprime, primepi def A145522(n): total = 0 for p in count(2): if 2**p > A145521(n): break if isprime(p): total += primepi(integer_nthroot(A145521(n), p)[0]) return total # Jason Yuen, Jan 31 2024 CROSSREFS Cf. A053810, A145521, A000720, A060967. Sequence in context: A194909 A038722 A277881 * A283939 A293056 A131968 Adjacent sequences: A145519 A145520 A145521 * A145523 A145524 A145525 KEYWORD nonn,more AUTHOR Leroy Quet, Oct 12 2008 EXTENSIONS a(11)-a(28) from Ray Chandler, Nov 01 2008 a(29)-a(32) from Jinyuan Wang, Feb 25 2020 a(33)-a(39) from Jason Yuen, Jan 31 2024 STATUS approved

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Last modified August 4 13:27 EDT 2024. Contains 374921 sequences. (Running on oeis4.)