A331288 a(n) = min(n, A225546(n)).

1, 2, 3, 3, 5, 6, 7, 6, 9, 10, 11, 12, 13, 14, 15, 5, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 10, 33, 34, 35, 27, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 20, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 15, 65, 66, 67, 68, 69, 70, 71, 54, 73, 74, 75, 76, 77, 78, 79, 80, 25, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 40

Offset: 1

Author

Antti Karttunen, Jan 20 2020

Keywords

• nonn

Comments

For all i, j:

a(i) = a(j) => A331287(i) = A331287(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A225546, A225547, A331301, A331287.

Programs

Mathematica

Array[If[# == 1, 1, Min[#, Times @@ Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]]] &, 96] (* Michael De Vlieger, Jan 21 2020 *)

PARI

A331288(n) = min(n, A225546(n));

PARI

A019565(n) = factorback(vecextract(primes(logint(n+!n, 2)+1), n));
A225546(n) = { my(f=factor(n)); for (i=1, #f~, my(p=f[i, 1]); f[i, 1] = A019565(f[i, 2]); f[i, 2] = 2^(primepi(p)-1); ); factorback(f); }; \\ From A225546
\\ If the following returns 1, then it is certainly true that A225546(p^e) > n (where p^e is one of the divisors of n), thus A225546(n) > n follows:
is_certainly_gt(p,e,n) = { my(b=A019565(e),j=(primepi(p)-1)); if(b>n,1,if((logint(b,2)*j)>logint(n,2),1,0)); };
A331288(n) = if((1==n)||isprime(n),n,my(f=factor(n)); for(i=1,#f~,if(is_certainly_gt(f[i,1],f[i,2],n),return(n))); min(n, A225546(n)));