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A244413 Exponent of highest power of 8 dividing n. 7
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,64

COMMENTS

This is the member g = 8 in the g-family of sequences, g integer >= 2, call it phi(g,n), n >= 1. In the Mahler reference, Lemma 2, pp. 6-7, this exponent is called f = -phi if g divides r = n (s = 1 there), and f = 0 if g does not divide r = n (s = 1 there).

REFERENCES

Kurt Mahler, p-adic numbers and their functions, 2nd ed., Cambridge University press, 1981

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65536

FORMULA

n = 8^a(n)*m with a(n) nonnegative integer such that 8 does not divide m, for n >= 1.

O.g.f.: Sum_{k>=1} x^(8^k)/(1-x^(8^k)).

MATHEMATICA

Table[IntegerExponent[n, 8], {n, 1, 100}] (* Amiram Eldar, Sep 14 2020 *)

PROG

(PARI) A244413(n) = valuation(n, 8); \\ Antti Karttunen, Oct 07 2017

CROSSREFS

Cf. A007814, A007949, A235127, A112765, A122841, A214411.

Sequence in context: A327170 A024362 A104488 * A318655 A056626 A290081

Adjacent sequences:  A244410 A244411 A244412 * A244414 A244415 A244416

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 27 2014

STATUS

approved

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)