A328219 LCM of the prime indices of n, all plus 1.

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

Offset: 1

Author

Gus Wiseman, Oct 16 2019

Keywords

• nonn

Comments

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.

Crossrefs

Sorted positions of first appearances are A328451.

LCM of prime indices is A290103.

LCM of prime indices minus 1 is A328456.

GCD of prime indices plus 1 is A328169.

Partitions whose parts plus 1 are relatively prime are A318980.

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

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

Programs

Mathematica

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

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A290103(n) = lcm(apply(p->primepi(p),factor(n)[,1]));
A328219(n) = A290103(A003961(n)); \\ Antti Karttunen, Oct 18 2019

Formula

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

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