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A244043
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Numbers n for new peaks of floor(sigma(n)/primepi(n)).
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1
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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
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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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(n-1) such that A(k) > A(a(n-1)). - Wolfdieter Lang, Jul 03 2014
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EXAMPLE
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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.
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MATHEMATICA
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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]] (* Jean-François Alcover, Jan 12 2018 *)
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PROG
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(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++); }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Edited. Crossrefs for sigma and primepi added. - Wolfdieter Lang, Jul 03 2014
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STATUS
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approved
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