login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162641 Number of even exponents in canonical prime factorization of n. 6
0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,36

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = A001221(n) - A162642(n).

a(A002035(n)) = 0.

a(A072587(n)) > 0.

Additive with a(p^e) = A059841(e). - Antti Karttunen, Jul 23 2017

From Antti Karttunen, Nov 28 2017: (Start)

a(n) = A162642(A003557(n)).

a(n) <= A056170(n).

(End)

MATHEMATICA

Table[Count[FactorInteger[n][[All, -1]], _?EvenQ], {n, 105}] (* Michael De Vlieger, Jul 23 2017 *)

PROG

(PARI) A162641(n) = omega(n) - omega(core(n)); \\ Antti Karttunen, Jul 23 2017

(Scheme) (define (A162641 n) (if (= 1 n) 0 (+ (A059841 (A067029 n)) (A162641 (A028234 n))))) ;; Antti Karttunen, Jul 23 2017

CROSSREFS

Cf. A001221, A003557, A002035, A007913, A025487, A059841, A061742 (where records occur), A072587, A162642.

Cf. A268335 (positions of zeros), A295316.

Sequence in context: A256574 A304819 A304820 * A185374 A087781 A181009

Adjacent sequences:  A162638 A162639 A162640 * A162642 A162643 A162644

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 08 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 04:03 EDT 2019. Contains 327119 sequences. (Running on oeis4.)