A360325 a(n) is the largest divisor of n that has only prime-indexed prime factors.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A006450, A076610, A320628, A360326, A360327, A360329.

Sequence in context: A137758 A340530 A147754 * A084305 A347066 A099375

Adjacent sequences: A360322 A360323 A360324 * A360326 A360327 A360328

Keyword

nonn,mult

Author

Amiram Eldar, Feb 03 2023

Status

approved