A347892 -id:A347892 - cp's OEIS frontend

A338539 Numbers having exactly two non-unitary prime factors.

36, 72, 100, 108, 144, 180, 196, 200, 216, 225, 252, 288, 300, 324, 360, 392, 396, 400, 432, 441, 450, 468, 484, 500, 504, 540, 576, 588, 600, 612, 648, 675, 676, 684, 700, 720, 756, 784, 792, 800, 828, 864, 882, 936, 968, 972, 980, 1000, 1008, 1044, 1080, 1089

Offset: 1

Amiram Eldar, Nov 01 2020

nonn

Numbers k such that A056170(k) = A001221(A057521(k)) = 2.
Numbers divisible by the squares of exactly two distinct primes.
Subsequence of A036785 and first differs from it at n = 44.
The asymptotic density of this sequence is (3/Pi^2)*(eta_1^2 - eta_2) = 0.0532928864..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).

			36 = 2^2 * 3^2 is a term since it has exactly 2 prime factors, 2 and 3, that are non-unitary.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Carl Pomerance and Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2011), pp. 52-66. See pp. 61-62.

Subsequence of A013929 and A036785.
Cf. A001221, A056170, A057521, A190641, A338540, A338541, A338542, A347892 (subsequence).
Cf. A154945 (eta_1), A324833 (eta_2).

Select[Range[1000], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 2 &]

A348499 Numbers k such that A003968(k) is a multiple of k, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119

Offset: 1

Antti Karttunen, Oct 29 2021

nonn

This is a subsequence of A333634. See comments in A347892.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Union of A005117 and A347892 (terms that are not squarefree).
Subsequence of A333634.
Positions of ones in A348037.
Cf. A003968, A348030, A348036, A347960.

f[p_, e_] := p*(p + 1)^(e - 1); s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[120], Divisible[s[#], #] &] (* Amiram Eldar, Oct 29 2021 *)

A003968(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
isA348499(n) = !(A003968(n)%n);

cp's OEIS Frontend

A338539 Numbers having exactly two non-unitary prime factors.

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