A356021 Positive numbers k such that, for any consecutive prime numbers p, q <= A006530(n), the p-adic and q-adic valuations of n are different.

1, 2, 3, 4, 8, 9, 10, 12, 16, 18, 20, 21, 24, 27, 32, 40, 45, 48, 50, 54, 63, 64, 72, 75, 80, 81, 84, 90, 96, 100, 108, 110, 126, 128, 135, 144, 147, 160, 162, 168, 189, 192, 200, 220, 243, 250, 256, 270, 273, 288, 300, 320, 324, 336, 350, 360, 375, 378, 384

Offset

1,2

Comments

Equivalently, these are fixed points of A356014.

This sequence is infinite as it contains A066205 and A066206.

If m is a term, then m^k is a term (for any k >= 0).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) local F, i, q, r;
  F:= sort(ifactors(n)[2], (a, b) -> a[1]<b[1] );
  if F[1][1] > 3 then return false fi;
  for i from 1 to nops(F)-1 do
    q:= nextprime(F[i][1]);
    if F[i+1][1] = q then if F[i][2]=F[i+1][2] then return false fi
    elif F[i+1][1] > nextprime(q) then return false
    fi;
  od;
  true
end proc:
filter(1):= true:
select(filter, [$1..500]); # Robert Israel, Apr 01 2026

Prog

(PARI) is(n) = { my (v=-1); forprime (p=2, oo, if (n==1, return (1), v==v=valuation(n, p), return (0), n\=p^v)) }

Crossrefs

Cf. A006530, A066205, A066206, A356014.

Sequence in context: A329268 A288860 A362930 * A132115 A230998 A184810

Adjacent sequences: A356018 A356019 A356020 * A356022 A356023 A356024

Keyword

nonn

Author

Rémy Sigrist, Jul 23 2022

Status

approved