A327167 a(n) = Product_{d|A276086(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the highest exponent of d dividing n.

1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 8, 1, 1, 1, 1, 2, 2, 1, 1, 1, 6, 1, 5, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 12, 1, 1, 1, 3, 6, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 2, 8, 1, 1, 1, 1, 48, 1, 2, 1, 1, 2, 7, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 6, 3, 3, 1, 1, 1, 1, 128

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = Product_{d|A276086(n), d>1} A008578(1+A286561(n,d)).

Other identities. For all n >= 1:

1+A001222(a(n)) = A327168(n).

Prog

(PARI)
A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };
A327167(n) = { my(m=1, v); fordiv(A276086(n), d, if((d>1) && ((v = valuation(n, d))>0), m *= prime(v))); (m); };

Crossrefs

Cf. A008578, A276086, A286561, A327168.

Cf. also A293514, A322312, A323155, A327154, A327155, A327156.

Sequence in context: A070084 A352635 A325937 * A268372 A361754 A298848

Adjacent sequences: A327164 A327165 A327166 * A327168 A327169 A327170

Keyword

nonn

Author

Antti Karttunen, Sep 19 2019

Status

approved