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.

A316431 Least common multiple divided by greatest common divisor of the integer partition with Heinz number n > 1.

This page as a plain text file.
%I A316431 #24 Sep 23 2018 21:27:09
%S A316431 1,1,1,1,2,1,1,1,3,1,2,1,4,6,1,1,2,1,3,2,5,1,2,1,6,1,4,1,6,1,1,10,7,
%T A316431 12,2,1,8,3,3,1,4,1,5,6,9,1,2,1,3,14,6,1,2,15,4,4,10,1,6,1,11,2,1,2,
%U A316431 10,1,7,18,12,1,2,1,12,6,8,20,6,1,3,1,13,1,4,21,14,5,5,1,6,6,9,22,15,24,2,1,4,10,3,1,14,1,6,12
%N A316431 Least common multiple divided by greatest common divisor of the integer partition with Heinz number n > 1.
%C A316431 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A316431 Antti Karttunen, <a href="/A316431/b316431.txt">Table of n, a(n) for n = 2..65537</a>
%H A316431 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A316431 <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%F A316431 a(n) = A290103(n)/A289508(n).
%F A316431 a(n) = a(A005117(n)). - _David A. Corneth_, Sep 06 2018
%e A316431 63 is the Heinz number of (4,2,2), which has LCM 4 and GCD 2, so a(63) = 4/2 = 2.
%e A316431 91 is the Heinz number of (6,4), which has LCM 12 and GCD 2, so a(91) = 12/2 = 6.
%t A316431 Table[With[{pms=Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]]},LCM@@pms/GCD@@pms],{n,2,100}]
%o A316431 (PARI) A316431(n) = if(1==n,1,my(pis = apply(p -> primepi(p), factor(n)[, 1]~)); lcm(pis)/gcd(pis)); \\ _Antti Karttunen_, Sep 06 2018
%Y A316431 Cf. A005117, A056239, A074761, A289508, A289509, A290103, A296150, A316429, A316430, A316437.
%K A316431 nonn,look
%O A316431 2,5
%A A316431 _Gus Wiseman_, Jul 02 2018
%E A316431 More terms from _Antti Karttunen_, Sep 06 2018