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A096067 Number of 3-smooth numbers between successive numbers that are powers of 2 or of 3. 1
0, 0, 0, 1, 0, 1, 2, 0, 3, 1, 2, 4, 0, 5, 2, 3, 6, 0, 6, 5, 2, 8, 2, 6, 8, 1, 10, 4, 6, 11, 0, 11, 8, 4, 13, 3, 10, 12, 2, 15, 6, 9, 16, 0, 17, 9, 8, 18, 2, 16, 14, 5, 20, 6, 14, 19, 2, 22, 10, 12, 23, 1, 22, 16, 8, 25, 6, 19, 22, 4, 27, 11, 16, 28, 0, 29, 16, 13, 30, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

a(n) = {k: A006899(n) < A003586(k) < A006899(n+1)}.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..10000

EXAMPLE

n=16: there are three 3-smooth numbers between A006899(16)=3^6=729 and A006899(17)=2^10=1024: A003586(38)=2^8*3=768, A003586(39)=2^5*3^3=864 and A003586(40)=2^2*3^5=972, therefore a(16)=3.

PROG

(PARI) \\ here spi(n) is A071521(n).

spi(n)={sum(k=0, logint(n, 3), logint(n\3^k, 2)+1)}

seq(n)={my(a=vector(n), p=1, s=1); for(i=1, #a, p=min(2^(1+logint(p, 2)), 3^(1+logint(p, 3))); my(t=spi(p)); a[i]=t-s-1; s=t); a} \\ Andrew Howroyd, Jan 07 2020

CROSSREFS

Cf. A003586, A006899, A071521.

Sequence in context: A133925 A071492 A259598 * A098861 A177878 A125940

Adjacent sequences:  A096064 A096065 A096066 * A096068 A096069 A096070

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 21 2004

EXTENSIONS

Terms a(40) and beyond from Andrew Howroyd, Jan 06 2020

STATUS

approved

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)