This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118306 #61 Dec 29 2023 12:52:52
%S A118306 1,3,2,9,7,15,5,27,4,21,13,45,11,33,6,81,19,75,17,63,10,39,29,135,49,
%T A118306 51,8,99,23,105,37,243,14,57,77,225,31,69,22,189,43,165,41,117,12,87,
%U A118306 53,405,25,147,26,153,47,375,91,297,34,93,61,315,59,111,20,729,119,195,71
%N A118306 If n = product{k>=1} p(k)^b(n,k), where p(k) is the k-th prime and where each b(n,k) is a nonnegative integer, then: If n occurs earlier in the sequence, then a(n) = product{k>=2} p(k-1)^b(n,k); If n does not occur earlier in the sequence, then a(n) = product{k>=1} p(k+1)^b(n,k).
%C A118306 Sequence is a permutation of the positive integers and it is its own inverse permutation.
%C A118306 From _Antti Karttunen_, Nov 05 2016: (Start)
%C A118306 A016945 gives the positions of even terms.
%C A118306 A007310 is closed with respect to this permutation. See A277911 for the permutation induced.
%C A118306 A029744 (without 3) seems to give the positions of records in this sequence (note that it gives the record positions in related A003961 and A048673) which implies that A083658 (without its term 5) would then give the record values.
%C A118306 (End)
%H A118306 Antti Karttunen, <a href="/A118306/b118306.txt">Table of n, a(n) for n = 1..10000</a>
%H A118306 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A118306 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#prime_indices">Index entries for sequences computed from prime indices</a>
%F A118306 From _Antti Karttunen_, Nov 05 2016: (Start)
%F A118306 a(1) = 1; and for n > 1, if n = a(k) for some k = 1 .. n-1, then a(n) = A064989(n), otherwise a(n) = A003961(n). [After the original definition and _R. J. Mathar_'s Maple-code]
%F A118306 a(1) = 1, and for n > 1, if A055396(n) is odd, a(n) = A003961(n), otherwise a(n) = A064989(n). [The above reduces to this.]
%F A118306 a(n) = product{k>=1} prime(k-((-1)^A055396(n)))^e(k) when n = product{k>=1} prime(k)^e(k).
%F A118306 a(2n) = A249734(n) and a(A249734(n)) = 2n.
%F A118306 A126760(a(A007310(n))) = A277911(n).
%F A118306 For n > 1, A055396(a(n)) = A055396(n) - (-1)^A055396(n). [Permutation sends the terms on any odd row of A246278 to the next even row just below, and vice versa.]
%F A118306 A246277(a(n)) = A246277(n). [While keeping them in the same column.]
%F A118306 a(n) = A064989(A064989(a(A003961(A003961(n))))).
%F A118306 (End)
%p A118306 A064989 := proc(n) local a,ifs,p ; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do if op(1,p) > 2 then a := a* prevprime(op(1,p))^op(2,p) ; fi ; od; RETURN(a) ; end: A003961 := proc(n) local a,ifs,p ; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do a := a* nextprime(op(1,p))^op(2,p) ; od; RETURN(a) ; end: A118306 := proc(nmin) local a,anxt,i,n ; a := [1] ; while nops(a) < nmin do n := nops(a)+1 ; if n in a then anxt := A064989(n) ; else anxt := A003961(n) ; fi ; a := [op(a),anxt] ; od; a ; end: A118306(100) ; # _R. J. Mathar_, Sep 06 2007
%o A118306 (PARI)
%o A118306 A118306(n) = { if(1==n, 1, my(f = factor(n)); my(d = (-1)^primepi(f[1, 1])); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-d)); factorback(f)); }; \\ _Antti Karttunen_, Nov 06 2016
%o A118306 for(n=1, 10001, write("b118306.txt", n, " ", A118306(n)));
%o A118306 (Scheme) (define (A118306 n) (cond ((= 1 n) n) ((odd? (A055396 n)) (A003961 n)) (else (A064989 n)))) ;; _Antti Karttunen_, Nov 05 2016
%Y A118306 Cf. A003961, A064989, A007310, A016945, A029744, A048673, A055396, A083221, A083658, A246277, A246278, A249734, A277911.
%K A118306 nonn,look
%O A118306 1,2
%A A118306 _Leroy Quet_, May 14 2006
%E A118306 More terms from _R. J. Mathar_, Sep 06 2007
%E A118306 A small omission in the definition corrected by _Antti Karttunen_, Nov 05 2016