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

1,2

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.

Links

Table of n, a(n) for n=1..74.

Formula

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

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

Mathematica

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

Prog

(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

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.

Sequence in context: A006047 A285712 A062068 * A328879 A130542 A128502

Adjacent sequences: A328216 A328217 A328218 * A328220 A328221 A328222

Keyword

nonn

Author

Gus Wiseman, Oct 16 2019

Status

approved