A371601 Nonsquarefree numbers whose largest nonunitary prime divisor is smaller than their smallest unitary prime divisor, if it exists.

4, 8, 9, 12, 16, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 52, 56, 60, 63, 64, 68, 72, 76, 80, 81, 84, 88, 92, 96, 99, 100, 104, 108, 112, 116, 117, 120, 121, 124, 125, 128, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 164, 168, 169, 171, 172, 175, 176

Offset

1,1

Comments

Subsequence of A283050 and first differs from it at n = 100: A283050(100) = 300 = 2^2 * 3 * 5^2 is not a term of this sequence.

Powerful numbers and nonpowerful numbers k such that 1 < A249740(k) < A277698(k), or equivalently, 1 < A006530(A057521(k)) < A020639(A055231(k)).

The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} f(p)/(p^2-p+1) = 0.32131800923..., where f(p) = Product_{primes q <= p} (q^2-q+1)/(q^2-1).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[e] > 1 && (Min[e] > 1 || Max[e[[FirstPosition[e, 1][[1]] ;; -1]]] == 1)]; Select[Range[200], q]

Prog

(PARI) is(n) = {my(e = apply(x->if(x > 1, 2, 1), factor(n)[, 2])); n > 1 && vecmax(e) > 1 && vecsort(e, , 4) == e; }

Crossrefs

Subsequence of A013929 and A283050.

Cf. A001694, A006530, A020639, A052485, A055231, A057521, A059956, A249740, A277698.

Sequence in context: A057109 A369639 A069189 * A283050 A069168 A374037

Adjacent sequences: A371598 A371599 A371600 * A371602 A371603 A371604

Keyword

nonn,easy

Author

Amiram Eldar, Mar 29 2024

Status

approved