A316431 - OEIS

%I #24 Sep 23 2018 21:27:09

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

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%H Antti Karttunen, <a href="/A316431/b316431.txt">Table of n, a(n) for n = 2..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>

%F a(n) = A290103(n)/A289508(n).

%F a(n) = a(A005117(n)). - _David A. Corneth_, Sep 06 2018

%e 63 is the Heinz number of (4,2,2), which has LCM 4 and GCD 2, so a(63) = 4/2 = 2.

%e 91 is the Heinz number of (6,4), which has LCM 12 and GCD 2, so a(91) = 12/2 = 6.

%t Table[With[{pms=Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]]},LCM@@pms/GCD@@pms],{n,2,100}]

%o (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 Cf. A005117, A056239, A074761, A289508, A289509, A290103, A296150, A316429, A316430, A316437.

%K nonn,look

%O 2,5

%A _Gus Wiseman_, Jul 02 2018

%E More terms from _Antti Karttunen_, Sep 06 2018