A331736 The largest odd divisor of A225546(n).

1, 1, 1, 3, 1, 1, 1, 3, 9, 1, 1, 3, 1, 1, 1, 5, 1, 9, 1, 3, 1, 1, 1, 3, 81, 1, 9, 3, 1, 1, 1, 5, 1, 1, 1, 27, 1, 1, 1, 3, 1, 1, 1, 3, 9, 1, 1, 5, 6561, 81, 1, 3, 1, 9, 1, 3, 1, 1, 1, 3, 1, 1, 9, 15, 1, 1, 1, 3, 1, 1, 1, 27, 1, 1, 81, 3, 1, 1, 1, 5, 25, 1, 1, 3, 1, 1, 1, 3, 1, 9, 1, 3, 1, 1, 1, 5, 1, 6561, 9, 243, 1, 1, 1, 3, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..1680

Formula

Multiplicative, with a(prime(i)^j) = A000265(A019565(j))^A000079(i-1).

Equally, with a(prime(i)^j) = A019565(A052928(j))^A000079(i-1).

a(n) = A000265(A225546(n)).

a(n) = A225546(A008833(n)).

Mathematica

Array[#/2^IntegerExponent[#, 2] &@ If[# == 1, 1, Times @@ Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]] &, 105] (* Michael De Vlieger, Feb 12 2020 *)

Prog

(PARI)
A019565(n) = factorback(vecextract(primes(logint(n+!n, 2)+1), n));
A331736(n) = { my(f=factor(n)); for (i=1, #f~, my(p=f[i, 1]); f[i, 1] = A019565((f[i, 2]>>1)<<1); f[i, 2] = 2^(primepi(p)-1); ); factorback(f); };
(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331736(n) = if(1==n, 1, my(f=factor(n), u=#binary(vecmax(f[, 2])), prods=vector(u, x, 1), m=2, e); for(i=2, u, for(k=1, #f~, if(bitand(f[k, 2], m), prods[i] *= f[k, 1])); m<<=1); prod(i=2, u, prime(i)^A048675(prods[i])));

Crossrefs

Cf. A000265, A005117, A008833, A052928, A225546.

Sequence in context: A293669 A055210 A082553 * A344300 A323840 A195644

Adjacent sequences: A331733 A331734 A331735 * A331737 A331738 A331739

Keyword

nonn,mult

Author

Antti Karttunen, Feb 02 2020

Status

approved