login
A360325
a(n) is the largest divisor of n that has only prime-indexed prime factors.
4
1, 1, 3, 1, 5, 3, 1, 1, 9, 5, 11, 3, 1, 1, 15, 1, 17, 9, 1, 5, 3, 11, 1, 3, 25, 1, 27, 1, 1, 15, 31, 1, 33, 17, 5, 9, 1, 1, 3, 5, 41, 3, 1, 11, 45, 1, 1, 3, 1, 25, 51, 1, 1, 27, 55, 1, 3, 1, 59, 15, 1, 31, 9, 1, 5, 33, 67, 17, 3, 5, 1, 9, 1, 1, 75, 1, 11, 3, 1
OFFSET
1,3
LINKS
FORMULA
a(n) = 1 if and only if n is in A320628.
a(n) = n if and only if n is in A076610.
a(n) = n/A360329(n).
Multiplicative with a(p^e) = p^e if p is a prime-indexed prime (A006450), and 1 otherwise.
MATHEMATICA
f[p_, e_] := If[PrimeQ[PrimePi[p]], p^e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(isprime(primepi(f[i, 1])), f[i, 1]^f[i, 2], 1)); }
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Feb 03 2023
STATUS
approved