cp's OEIS Frontend

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.

A351168 If n = p_1^e_1 * ... * p_k^e_k, where p_1 < ... < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k - 1)^e_k; a(1) = 1.

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%I A351168 #67 Feb 11 2022 15:01:35
%S A351168 1,1,2,1,4,4,6,1,4,8,10,8,12,12,12,1,16,8,18,16,18,20,22,16,16,24,8,
%T A351168 24,28,24,30,1,30,32,30,16,36,36,36,32,40,36,42,40,36,44,46,32,36,32,
%U A351168 48,48,52,16,50,48,54,56,58,48,60,60,54,1,60,60,66,64,66,60,70,32,72,72,48
%N A351168 If n = p_1^e_1 * ... * p_k^e_k, where p_1 < ... < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k - 1)^e_k; a(1) = 1.
%C A351168 First time a term appears four or more times in a row is when n = 1684.
%H A351168 Amiram Eldar, <a href="/A351168/b351168.txt">Table of n, a(n) for n = 1..10000</a>
%H A351168 Jan Misali, <a href="https://www.seximal.net/names-of-other-bases">What should we call the other bases?</a>, Web page, no date. Inspiration for this sequence.
%F A351168 a(n) = n*(1 - 1/p_k)^e_k where prime factorization n = p_1^e_1 * ... * p_k^e_k with ascending p_1 < ... < p_k.
%F A351168 a(n) = n*(1 - 1/A006530(n))^A071178(n).
%e A351168 The prime factorization of 44 is 2^2 * 11^1, so a(44) = 2^2 * 10^1 = 40.
%e A351168 The prime factorization of 50 is 2^1 * 5^2, so a(50) = 2^1 * 4^2 = 32.
%t A351168 a[n_] := Module[{f = FactorInteger[n]}, n*(1 - 1/f[[-1, 1]])^f[[-1, 2]]]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Feb 04 2022 *)
%o A351168 (PARI) a(n) = my(f=factor(n),r=matsize(f)[1]); if(r, f[r,1]--); factorback(f); \\ _Kevin Ryde_, Feb 03 2022
%Y A351168 Cf. A006530 (greatest prime), A071178 (its exponent).
%Y A351168 Cf. A171462 (one instance of the decrement), A003958 (all primes decremented), A351419, A351425.
%K A351168 nonn
%O A351168 1,3
%A A351168 _Ben Polson_, Feb 03 2022
%E A351168 a(1) = 1 prepended by _Michel Marcus_, Feb 04 2022
%E A351168 Edited by _N. J. A. Sloane_, Feb 11 2022