The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A110085

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A110085

Numbers k such that sigma(k) - phi(k) < tau(k)^omega(k), where sigma = A000203, phi = A000010, tau = A000005 and omega = A001221.
(history; published version)

#14 by Michel Marcus at Sun Sep 15 02:39:54 EDT 2024

STATUS

reviewed

approved

#13 by Joerg Arndt at Sun Sep 15 01:40:59 EDT 2024

STATUS

proposed

reviewed

#12 by Amiram Eldar at Sun Sep 15 00:57:16 EDT 2024

STATUS

editing

proposed

#11 by Amiram Eldar at Sun Sep 15 00:30:56 EDT 2024

MATHEMATICA

q[k_] := DivisorSigma[1, k] - EulerPhi[k] < DivisorSigma[0, k]^PrimeNu[k]; Select[Range[300], q] (* Amiram Eldar, Sep 15 2024 *)

#10 by Amiram Eldar at Sun Sep 15 00:28:24 EDT 2024

NAME

Numbers n k such that sigma(nk) - phi(nk) < tau(nk)^omega(nk), where sigma = A000203, phi = A000010, tau = A000005 and omega = A001221.

COMMENTS

A051612(a(n)) < A110088(a(n)); intersection of A018252 and A110086.

FORMULA

A051612(a(n)) < A110088(a(n)).

CROSSREFS

Intersection of A018252 and A110086

Cf. A000005, A000010, A000203, A001221, A051612, A110087, A110088.

STATUS

approved

editing

#9 by Reinhard Zumkeller at Tue Aug 05 15:01:47 EDT 2014

STATUS

editing

approved

#8 by Reinhard Zumkeller at Tue Aug 05 11:10:24 EDT 2014

PROG

(Haskell)

a110085 n = a110085_list !! (n-1)

a110085_list = filter (\x -> a051612 x < a110088 x) [1..]

-- Reinhard Zumkeller, Aug 05 2014

#7 by Reinhard Zumkeller at Tue Aug 05 11:09:34 EDT 2014

LINKS

Reinhard Zumkeller, <a href="/A110085/b110085.txt">Table of n, a(n) for n = 1..1000</a>

STATUS

approved

editing

#6 by Charles R Greathouse IV at Thu Feb 14 17:45:54 EST 2013

STATUS

editing

approved

#5 by Charles R Greathouse IV at Thu Feb 14 17:44:38 EST 2013

PROG

(PARI) is(n)=sigma(n)-eulerphi(n)<numdiv(n)^omega(n) \\ Charles R Greathouse IV, Feb 14 2013

STATUS

approved

editing