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A336915 a(n) is the exponent of the least power of 2 that when multiplied by n, makes the product nondeficient, or -1 if n itself is a power of 2. 7
-1, -1, 1, -1, 2, 0, 2, -1, 1, 1, 3, 0, 3, 1, 1, -1, 4, 0, 4, 0, 1, 2, 4, 0, 2, 2, 1, 0, 4, 0, 4, -1, 1, 3, 1, 0, 5, 3, 1, 0, 5, 0, 5, 1, 1, 3, 5, 0, 2, 1, 1, 1, 5, 0, 2, 0, 1, 3, 5, 0, 5, 3, 1, -1, 2, 0, 6, 2, 1, 0, 6, 0, 6, 4, 1, 2, 2, 0, 6, 0, 1, 4, 6, 0, 2, 4, 1, 0, 6, 0, 2, 2, 1, 4, 2, 0, 6, 1, 1, 0, 6, 0, 6, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Number of iterations of x -> 2x needed before the result is nondeficient (sigma(x) >= 2x), when starting from x=n, or -1 if a nondeficient number would never be reached (when n is a power of 2).

If neither x and y are powers of 2, and gcd(x,y) = 1, then a(x*y) <= min(a(x),a(y)). Compare to a similar comment in A336835.

LINKS

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

FORMULA

For odd primes p, a(p) = A000523(p).

PROG

(PARI) A336915(n) = if(!bitand(n, n-1), -1, for(i=0, oo, my(n2 = n+n); if(sigma(n) >= n2, return(i)); n = n2));

CROSSREFS

Cf. A000523, A005940, A336834, A336916 (same sequence + 1).

Cf. also A279048, A336835.

Sequence in context: A328775 A053250 A302242 * A236627 A116664 A295672

Adjacent sequences:  A336912 A336913 A336914 * A336916 A336917 A336918

KEYWORD

sign

AUTHOR

Antti Karttunen, Aug 08 2020

STATUS

approved

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Last modified August 4 19:03 EDT 2021. Contains 346455 sequences. (Running on oeis4.)