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.

A290106 a(1) = 1; for n > 1, if n = Product prime(k)^e(k), then a(n) = Product (k)^(e(k)-1).

This page as a plain text file.
%I A290106 #14 Aug 15 2017 20:34:09
%S A290106 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,3,1,4,1,1,1,1,1,1,1,
%T A290106 1,2,1,1,1,1,1,1,1,1,2,1,1,1,4,3,1,1,1,4,1,1,1,1,1,1,1,1,2,1,1,1,1,1,
%U A290106 1,1,1,2,1,1,3,1,1,1,1,1,8,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,4,2,3,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,2,1,1,1
%N A290106 a(1) = 1; for n > 1, if n = Product prime(k)^e(k), then a(n) = Product (k)^(e(k)-1).
%H A290106 Antti Karttunen, <a href="/A290106/b290106.txt">Table of n, a(n) for n = 1..10000</a>
%H A290106 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A290106 Multiplicative with a(prime(k)^e) = k^(e-1).
%F A290106 a(n) = A003963(n) / A156061(n).
%F A290106 a(n) = A003963(A003557(n)) = A003963(n/A007947(n)).
%e A290106 For n = 21 = 3*7 = prime(2)^1 * prime(4)^1, a(n) = 2^0 * 4^0 = 1*1 = 1.
%e A290106 For n = 360 = 2^3 * 3^2 * 5^1 = prime(1)^3 * prime(2)^2 * prime(3)^1, a(n) = 1^2 * 2^1 * 3^0 = 1*2*1 = 2.
%t A290106 Table[If[n == 1, 1, Apply[Times, Map[PrimePi[#1]^#2 & @@ # &, #]] / Apply[Times, PrimePi[#[[All, 1]] ]]] &@ FactorInteger@ n, {n, 120}] (* _Michael De Vlieger_, Aug 14 2017 *)
%o A290106 (Scheme)
%o A290106 (define (A290106 n) (/ (A003963 n) (A156061 n)))
%o A290106 (define (A290106 n) (if (= 1 n) 1 (* (expt (A055396 n) (- (A067029 n) 1)) (A290106 (A028234 n)))))
%Y A290106 Cf. A003557, A003963, A007947, A156061, A290105.
%Y A290106 Differs from A290104 for the first time at n=21.
%K A290106 nonn,mult
%O A290106 1,9
%A A290106 _Antti Karttunen_, Aug 13 2017