

A328219


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


7



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
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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



