A352698 Numbers k such that A308485(k) is a multiple of k.

1, 2, 8, 9, 10, 12, 65, 142, 2539, 9027, 9905, 23634, 27638428

Offset

1,2

Comments

Numbers k such that the sum of integer logs of the composite numbers between prime(k) and prime(k+1) is divisible by k.

Links

Table of n, a(n) for n=1..13.

Example

a(3) = 8 is a term because prime(8) = 19 and prime(9) = 23, and the sum of integer logs of 20, 21 and 22 is 2*2+5+3+7+2+11 = 32 which is a multiple of 8.

Maple

f:= proc(m) local t; add(t[1]*t[2], t=ifactors(m)[2]) end proc:
t:= 0: n:= 0: p:= 2: count:= 0: R:= NULL:
for m from 3 to 10^6 do
  if isprime(m) then
     n:= n+1;
     if t mod n = 0 then R:= R, n; count:= count+1 fi;
     p:= m; t:= 0
  else
    t:= t+f(m)
  fi
od:
R;

Mathematica

f[m_] := Sum[t[[1]]*t[[2]], {t, FactorInteger[m]}];
t = 0; n = 0; p = 2; count = 0; R = {};
For[m = 3, m <= 10^6, m++, If[PrimeQ[m], n++; If[Mod[t, n] == 0, AppendTo[R, n]; count++]; p = m; t = 0, t = t+f[m]]];
R (* Jean-François Alcover, Mar 07 2024, translated from Maple code *)

Crossrefs

Cf. A001414, A308485.

Sequence in context: A356061 A167450 A050569 * A318175 A318182 A047469

Adjacent sequences: A352695 A352696 A352697 * A352699 A352700 A352701

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Mar 29 2022

Status

approved