OFFSET
1,2
COMMENTS
Completely multiplicative with a(2) = 2, a(3) = 3, a(prime(k)) = prime(k-1) * prime(k-2) for k > 2. - Andrew Howroyd & Antti Karttunen, Aug 04 2018
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10080
FORMULA
MATHEMATICA
a[n_] := a[n] = Module[{k, p, e}, Which[n<4, n, PrimeQ[n], k = PrimePi[n]; Prime[k-1] Prime[k-2], True, Product[{p, e} = pe; a[p]^e, {pe, FactorInteger[n]}]]];
a /@ Range[1, 72] (* Jean-François Alcover, Sep 20 2019 *)
f[p_, e_] := If[p < 5, p, NextPrime[p, -1]*NextPrime[p, -2]]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 01 2022 *)
PROG
(PARI)
A065330(n) = { while(0 == (n%2), n = n/2); while(0 == (n%3), n = n/3); n; }
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
(PARI) r(p) = {my(q = precprime(p-1)); q*precprime(q-1)};
a(n) = {my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]<5, f[i, 1], r(f[i, 1]))^f[i, 2])}; \\ Amiram Eldar, Dec 01 2022
(Scheme)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Dec 15 2015
EXTENSIONS
Keyword mult added by Antti Karttunen, Aug 04 2018
STATUS
approved