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A295664 Exponent of the highest power of 2 dividing number of divisors of n: a(n) = A007814(A000005(n)); 2-adic valuation of tau(n). 6
0, 1, 1, 0, 1, 2, 1, 2, 0, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 3, 0, 2, 2, 1, 1, 3, 1, 1, 2, 2, 2, 0, 1, 2, 2, 3, 1, 3, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 0, 2, 3, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 0, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 1, 3, 1, 3, 3, 2, 1, 2, 1, 3, 2, 1, 1, 3, 2, 1, 1, 2, 2, 4, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

In the prime factorization of n = p1^e1 * ... pk^ek, add together the number of trailing 1-bits in each exponent e when they are written in binary.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

FORMULA

Additive with a(p^e) = A007814(1+e).

a(1) = 0; for n > 1, a(n) = A007814(1+A067029(n)) + a(A028234(n)).

a(n) = A007814(A000005(n)).

a(n) >= A162642(n) >= A056169(n).

MATHEMATICA

Table[IntegerExponent[DivisorSigma[0, n], 2], {n, 120}] (* Michael De Vlieger, Nov 28 2017 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A295664 n) (if (= 1 n) 0 (+ (A007814 (+ 1 (A067029 n))) (A295664 (A028234 n)))))

(define (A295664 n) (A007814 (A000005 n)))

(PARI) a(n) = valuation(numdiv(n), 2); \\ Michel Marcus, Nov 30 2017

CROSSREFS

Cf. A000005, A007814, A028234, A056169, A067029, A162642, A295663.

Cf. A000290 (positions of zeros).

Sequence in context: A262115 A071460 A218867 * A250213 A033794 A218856

Adjacent sequences:  A295661 A295662 A295663 * A295665 A295666 A295667

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 28 2017

STATUS

approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)