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A297164 Permutation of nonnegative integers: a(n) = A156552(A005940(1+n)-1).

%I A297164 #12 Feb 28 2022 07:56:15
%S A297164 0,1,2,3,4,7,8,5,6,17,16,23,64,65,10,9,32,19,128,129,512,67,256,47,24,
%T A297164 4097,20,4099,32768,79,1024,11,18,31,14,29,4096,2049,66,515,514,263,
%U A297164 65536,2053,8388608,524289,16384,87,16777216,2097153,70,524291,17179869184,287,524288,1037,8388610,289,134217728,1071,520,97,38,15,12,257,8192,63
%N A297164 Permutation of nonnegative integers: a(n) = A156552(A005940(1+n)-1).
%C A297164 Note the indexing: although the domain starts from 1, the range includes also zero.
%H A297164 Antti Karttunen, <a href="/A297164/b297164.txt">Table of n, a(n) for n = 1..379</a>
%H A297164 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A297164 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A297164 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A297164 a(n) = A156552(A005940(1+n)-1).
%o A297164 (Scheme) (define (A297164 n) (A156552 (+ -1 (A005940 (+ 1 n)))))
%o A297164 (PARI)
%o A297164 A005940(n) = { my(p=2,t=1); n--; until(!n\=2, if(n%2, t*=p, p=nextprime(p+1))); t };
%o A297164 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A297164 A297164(n) = A156552(A005940(1+n)-1); \\ _Antti Karttunen_, Feb 27 2022
%Y A297164 Inverse: A297163.
%Y A297164 Cf. A005940, A156552.
%Y A297164 Cf. also A297166, A341520, A351960.
%K A297164 nonn
%O A297164 1,3
%A A297164 _Antti Karttunen_, Jan 05 2018