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A278908 Multiplicative with a(p^e) = 2^omega(e), where omega = A001221. 4
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The number of exponential unitary (or e-unitary) divisors of n and the number of exponential squarefree exponential divisors (or e-squarefree e-divisors) of n. These are divisors of n = Product p(i)^a(i) of the form Product p(i)^b(i) where each b(i) is a unitary divisor of a(i) in the first case, or each b(i) is a squarefree divisor of a(i) in the second case. - Amiram Eldar, Dec 29 2018

LINKS

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

X. Cao, W. Zhai, Some arithmetic functions involving exponential divisors, JIS 13 (2010) # 10.3.7, eq (20).

Nicusor Minculete and László Tóth, Exponential unitary divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 35 (2011), pp. 205-216.

Xiangzhen Zhao, Min Liu, and Yu Huang, Mean value for the function t^(e)(n) over square-full numbers, Scientia Magna, Vol. 8, No. 3 (2012), pp. 110-114.

Index entries for sequences computed from exponents in factorization of n

MAPLE

A278908 := proc(n)

    local a, p, e;

    a := 1;

    if n =1 then

        ;

    else

        for p in ifactors(n)[2] do

            e := op(2, p) ;

            a := a*2^A001221(e) ;

        end do:

    end if;

    a ;

end proc:

MATHEMATICA

Table[Times @@ Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 1 :> 2^PrimeNu[e]], {n, 105}] (* Michael De Vlieger, Jul 29 2017 *)

PROG

(Scheme) (define (A278908 n) (if (= 1 n) n (* (A000079 (A001221 (A067029 n))) (A278908 (A028234 n))))) ;; Antti Karttunen, Jul 27 2017

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = 2^omega(f[k, 2]); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Jul 28 2017

CROSSREFS

Cf. A001221.

Sequence in context: A291119 A007424 A323308 * A307848 A255326 A085424

Adjacent sequences:  A278905 A278906 A278907 * A278909 A278910 A278911

KEYWORD

nonn,easy,mult

AUTHOR

R. J. Mathar, Nov 30 2016

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)