

A244043


Numbers n for new peaks of floor(sigma(n)/primepi(n)).


1



2, 6, 12, 24, 30, 36, 60, 96, 120, 180, 240, 360, 600, 720, 840, 1080, 1260, 1680, 2520, 5040, 7560, 10080, 12600, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160
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OFFSET

1,1


COMMENTS

The sequence entries frequently are members of A002182 (highly composite numbers). Similar sequences can be generated by varying the "k" seen in the PARI code, for example to k=2.


LINKS



FORMULA

Define A(n) = floor(A000203(n)/A000720(n)) for n >= 2. Then a(1) = 2 and for n >= 2 a(n) is the least k > a(n1) such that A(k) > A(a(n1)).  Wolfdieter Lang, Jul 03 2014


EXAMPLE

Example at n=2 (start), sigma(2)=3, primepi(2)=1 so the initial peak is 3.
We see a new peak (4) at n=6 from floor(12/3), a(2)=6.
We see new peak (5) at n=12 from floor(28/5), a(3)=12. No entry is defined for n<2.


MATHEMATICA

Reap[For[peak = 0; n = 2, n < 10^5, n++, f = Floor[DivisorSigma[1, n] / PrimePi[n]]; If[f > peak, peak = f; Sow[n]]]][[2, 1]] (* JeanFrançois Alcover, Jan 12 2018 *)


PROG

(PARI) genit={my(maxx=100000); peak=3; k=1; n=3; optr=2; sptr=1;
write("A244043.csv", sptr, " , ", 2); while(n<maxx, a=primepi(n); b=sigma(n);
c=floor(b/a*1./k); optr++; if(c>peak, sptr++; peak=c;
write("A244043.csv", sptr, " , ", optr); ); n++); }


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS

Edited. Crossrefs for sigma and primepi added.  Wolfdieter Lang, Jul 03 2014


STATUS

approved



