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A285801 Numbers having at most one odd prime factor to an odd power in their prime factorization. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 63, 64, 67, 68, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 86, 88, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is of asymptotic density zero. It seems to grow faster than n*(log_10(n)-1), which is a fair approximation in the range 10^3 .. 10^6 or beyond, cf. examples.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10001

EXAMPLE

A285800(1) = 15 = 3*5 is the smallest positive integer to have two odd prime factors to an odd power (here 1) in its factorization, therefore it's the first number not in this sequence.

A285800(2) = 21 = 3*7, A285800(3) = 30 = 2*A285800(1) and A285800(3) = 33 = 3*11 are the next three numbers not in this sequence.

a(10) = 10, a(100) = 137, a(10^3) = 2066, a(10^4) = 29996, a(10^5) = 402878, a(10^6) = 5083823.

MAPLE

s800:=[]; s801:=[1];

for n from 2 to 1000 do

c:=0;

t2:=ifactors(n)[2];

for t3 in t2 do if t3[1]>2 and (t3[2] mod 2 = 1) then c:=c+1; fi; od:

if c <= 1 then s801:=[op(s801), n]; else s800:=[op(s800), n]; fi;

od:

s800; # A285800

s801; # A285801 - N. J. A. Sloane, Sep 30 2017

PROG

(PARI) is(n)=2>#select(t->bittest(t, 0), factor(n>>valuation(n, 2))[, 2])

CROSSREFS

Complement of A285800.

Sequence in context: A095736 A004829 A075592 * A324109 A070776 A320230

Adjacent sequences:  A285798 A285799 A285800 * A285802 A285803 A285804

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Apr 26 2017

STATUS

approved

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Last modified June 20 18:28 EDT 2021. Contains 345199 sequences. (Running on oeis4.)