A331735 a(n) = A009194(A225546(n)) = gcd(A225546(n), sigma(A225546(n))).

1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 12, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 4, 1, 3, 1, 12, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 12, 1, 9, 1, 4, 1, 1, 1, 10, 1, 3, 1, 1, 1, 1, 1, 12, 1

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..512

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A009194(A225546(n)) = gcd(A225546(n), A331733(n)).

Mathematica

Array[GCD[#, DivisorSigma[1, #]] &@ 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)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331735(n) = if(issquarefree(n), 1, my(f=factor(n), u=#binary(vecmax(f[, 2])), prods=vector(u, x, 1), m=1, e); for(i=1, u, for(k=1, #f~, if(bitand(f[k, 2], m), prods[i] *= f[k, 1])); m<<=1); gcd(prod(i=1, u, prime(i)^A048675(prods[i])), prod(i=1, u, (prime(i)^(1+A048675(prods[i]))-1)/(prime(i)-1))));

Crossrefs

Cf. A000203, A009194, A225546, A331733, A331734.

Sequence in context: A064793 A355925 A275109 * A345948 A346013 A344697

Adjacent sequences: A331732 A331733 A331734 * A331736 A331737 A331738

Keyword

nonn

Author

Antti Karttunen, Feb 04 2020

Status

approved