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 A348717 #28 May 20 2022 13:00:20
%S A348717 1,2,2,4,2,6,2,8,4,10,2,12,2,14,6,16,2,18,2,20,10,22,2,24,4,26,8,28,2,
%T A348717 30,2,32,14,34,6,36,2,38,22,40,2,42,2,44,12,46,2,48,4,50,26,52,2,54,
%U A348717 10,56,34,58,2,60,2,62,20,64,14,66,2,68,38,70,2,72,2
%N A348717 a(n) is the least k such that A003961^i(k) = n for some i >= 0 (where A003961^i denotes the i-th iterate of A003961).
%C A348717 All terms except a(1) = 1 are even.
%C A348717 To compute a(n) for n > 1:
%C A348717 - if n = Product_{j = 1..o} prime(p_j)^e_j (where prime(i) denotes the i-th prime number, p_1 < ... < p_o and e_1 > 0)
%C A348717 - then a(n) = Product_{j = 1..o} prime(p_j + 1 - p_1)^e_j.
%C A348717 This sequence has similarities with A304776: here we shift down prime indexes, there prime exponents.
%C A348717 Smallest number generated by uniformly decrementing the indices of the prime factors of n. Thus, for n > 1, the smallest m > 1 such that the first differences of the indices of the ordered prime factors (including repetitions) are the same for m and n. As a function, a(.) preserves properties such as prime signature. - _Peter Munn_, May 12 2022
%H A348717 Rémy Sigrist, <a href="/A348717/b348717.txt">Table of n, a(n) for n = 1..10000</a>
%H A348717 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A348717 a(n) = n iff n belongs to A004277.
%F A348717 A003961^(A055396(n)-1)(a(n)) = n for any n > 1.
%F A348717 a(n) = 2 iff n belongs to A000040 (prime numbers).
%F A348717 a(n) = 4 iff n belongs to A001248 (squares of prime numbers).
%F A348717 a(n) = 6 iff n belongs to A006094 (products of two successive prime numbers).
%F A348717 a(n) = 8 iff n belongs to A030078 (cubes of prime numbers).
%F A348717 a(n) = 10 iff n belongs to A090076.
%F A348717 a(n) = 12 iff n belongs to A251720.
%F A348717 a(n) = 14 iff n belongs to A090090.
%F A348717 a(n) = 16 iff n belongs to A030514.
%F A348717 a(n) = 30 iff n belongs to A046301.
%F A348717 a(n) = 32 iff n belongs to A050997.
%F A348717 a(n) = 36 iff n belongs to A166329.
%F A348717 a(1) = 1, for n > 1, a(n) = 2*A246277(n). - _Antti Karttunen_, Feb 23 2022
%F A348717 a(n) = A122111(A243074(A122111(n))). - _Peter Munn_, Feb 23 2022
%F A348717 From _Peter Munn_ and _Antti Karttunen_, May 12 2022: (Start)
%F A348717 a(1) = 1; a(2n) = 2n; a(A003961(n)) = a(n). [complete definition]
%F A348717 a(n) = A005940(1+A322993(n)) = A005940(1+A000265(A156552(n))).
%F A348717 Equivalently, A156552(a(n)) = A000265(A156552(n)).
%F A348717 A297845(a(n), A020639(n)) = n.
%F A348717 A046523(a(n)) = A046523(n).
%F A348717 A071364(a(n)) = A071364(n).
%F A348717 a(n) >= A071364(n).
%F A348717 A243055(a(n)) = A243055(n).
%F A348717 (End)
%t A348717 a[1] = 1; a[n_] := Module[{f = FactorInteger[n], d}, d = PrimePi[f[[1, 1]]] - 1; Times @@ ((Prime[PrimePi[#[[1]]] - d]^#[[2]]) & /@ f)]; Array[a, 100] (* _Amiram Eldar_, Oct 31 2021 *)
%o A348717 (PARI) a(n) = { my (f=factor(n)); if (#f~>0, my (pi1=primepi(f[1,1])); for (k=1, #f~, f[k,1] = prime(primepi(f[k,1])-pi1+1))); factorback(f) }
%Y A348717 Positions of particular values (see formula section): A000040, A001248, A006094, A030078, A030514, A046301, A050997, A090076, A090090, A166329, A251720.
%Y A348717 Also see formula section for the relationship to: A000265, A003961, A004277, A005940, A020639, A046523, A055396, A071364, A122111, A156552, A243055, A243074, A297845, A322993.
%Y A348717 Sequences with comparable definitions: A304776, A316437.
%Y A348717 Cf. A246277 (terms halved), A305897 (restricted growth sequence transform), A354185 (Möbius transform), A354186 (Dirichlet inverse), A354187 (sum with it).
%K A348717 nonn
%O A348717 1,2
%A A348717 _Rémy Sigrist_, Oct 31 2021