A328219 - OEIS

%I #12 Oct 18 2019 16:44:41

%S 1,2,3,2,4,6,5,2,3,4,6,6,7,10,12,2,8,6,9,4,15,6,10,6,4,14,3,10,11,12,

%T 12,2,6,8,20,6,13,18,21,4,14,30,15,6,12,10,16,6,5,4,24,14,17,6,12,10,

%U 9,22,18,12,19,12,15,2,28,6,20,8,30,20,21,6,22,26

%N LCM of the prime indices of n, all plus 1.

%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

%F a(n) = A290103(A003961(n)).

%F If n = A000040(i_1) * ... * A000040(i_k), then a(n) = lcm(1+i_1,...,1+i_k).

%t Table[If[n==1,1,LCM@@(PrimePi/@First/@FactorInteger[n]+1)],{n,100}]

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

%o A290103(n) = lcm(apply(p->primepi(p),factor(n)[,1]));

%o A328219(n) = A290103(A003961(n)); \\ _Antti Karttunen_, Oct 18 2019

%Y Sorted positions of first appearances are A328451.

%Y LCM of prime indices is A290103.

%Y LCM of prime indices minus 1 is A328456.

%Y GCD of prime indices plus 1 is A328169.

%Y Partitions whose parts plus 1 are relatively prime are A318980.

%Y Numbers whose prime indices plus 1 are relatively prime are A318981,

%Y Cf. A003961, A056239, A112798, A258409, A289508, A289509, A328167, A328168.

%K nonn

%O 1,2

%A _Gus Wiseman_, Oct 16 2019