The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348427 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A348427

Composite k for which sigma(k) is divisible by the sum of the arithmetic derivatives of the divisors of k.
(history; published version)

#13 by Charles R Greathouse IV at Thu Sep 08 08:46:26 EDT 2022

PROG

(MAGMAMagma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2]/Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [k:k in [2..10300]|not IsPrime(k) and DivisorSigma(1, k) mod &+[Floor(f(d)): d in Divisors(k)|d ne 1] eq 0];

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#12 by N. J. A. Sloane at Fri Nov 19 16:58:52 EST 2021

STATUS

proposed

approved

#11 by Michel Marcus at Tue Oct 19 03:40:39 EDT 2021

STATUS

editing

proposed

#10 by Michel Marcus at Tue Oct 19 03:40:09 EDT 2021

PROG

(PARI) ad(n) = if (n<1, 0, my(f = factor(n)); n*sum(k=1, #f~, f[k, 2]/f[k, 1])); \\ A003415

isok(k) = (k>1) && !isprime(k) && !(sigma(k) % sumdiv(k, d, ad(d))); \\ Michel Marcus, Oct 19 2021

STATUS

proposed

editing

#9 by Wesley Ivan Hurt at Mon Oct 18 17:35:24 EDT 2021

STATUS

editing

proposed

#8 by Wesley Ivan Hurt at Mon Oct 18 17:35:14 EDT 2021

EXAMPLE

10 is a term because sigma(10) = 1 + 2 + 5 + 10 = 18 is divisible by 1' + 2' + 5' + 10' = 0 + 1 + 1 + 7 = 9 = A319684(10).

33 is a term because sigma(33) = 1 + 3 + 11 + 33 = 48 is divisible by 1' + 3' + 11' + 33' = 0 + 1 + 1 + 14 = 16 = A319684(33).

STATUS

proposed

editing

#7 by Michel Marcus at Mon Oct 18 16:26:27 EDT 2021

STATUS

editing

proposed

#6 by Michel Marcus at Mon Oct 18 16:26:22 EDT 2021

PROG

(MAGMA) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2]/Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [k:k in [2..10300]|not IsPrime(k) and DivisorSigma(1, k) mod &+[Floor(f(d)): d in Divisors(k)|d ne 1] eq 0]; //

STATUS

proposed

editing

#5 by Amiram Eldar at Mon Oct 18 15:50:02 EDT 2021

STATUS

editing

proposed

#4 by Amiram Eldar at Mon Oct 18 15:49:58 EDT 2021

MATHEMATICA

d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); s[n_] := DivisorSum[n, d[#] &]; Select[Range[10000], CompositeQ[#] && Divisible[DivisorSigma[1, #], s[#]] &] (* Amiram Eldar, Oct 18 2021 *)

STATUS

proposed

editing