A366460 Odd terms in A366825.

45, 63, 99, 117, 153, 171, 175, 207, 261, 275, 279, 315, 325, 333, 369, 387, 423, 425, 475, 477, 495, 531, 539, 549, 575, 585, 603, 637, 639, 657, 693, 711, 725, 747, 765, 775, 801, 819, 833, 855, 873, 909, 925, 927, 931, 963, 981, 1017, 1025, 1035, 1071, 1075

Offset

1,1

Comments

Proper subset of A364997, in turn a proper subset of A364996, which is a proper subset of A126706.

Prime signature of a(n) is 2 followed by at least one 1.

Numbers of the form A065642(k) where k is an odd term in A120944.

Numbers of the form p^2 * m, squarefree m > 1, odd prime p < lpf(m), where lpf(m) = A020639(m).

The asymptotic density of this sequence is (2/(3*Pi^2)) * Sum_{p odd prime} ((1/p^2) * (Product_{odd primes q <= p} (q/(q+1)))) = 0.0537475047... . - Amiram Eldar, Jan 08 2024

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

{a(n)} = {A366825 \ A364999}.

Example

a(1) = 45 = 9*5 = p^2 * m, squarefree m > 1; sqrt(9) < lpf(5), i.e., 3 < 5.
a(2) = 63 = 9*7 = p^2 * m, squarefree m > 1; sqrt(9) < lpf(7), i.e., 3 < 7.
Prime powers p^k, k > 2, are not in the sequence since m = p^(k-2) is not squarefree and p = lpf(m).

Mathematica

Select[Select[Range[1, 1100, 2], PrimeOmega[#] > PrimeNu[#] > 1 &], And[OddQ[#1], #1/(Times @@ #2) == #2[[1]]] & @@ {#, FactorInteger[#][[All, 1]]} &]

Prog

(PARI) is(n) = {my(e); n%2 && e = factor(n)[, 2]; #e > 1 && e[1] == 2 && vecmax(e[2..#e]) == 1; } \\ Amiram Eldar, Jan 08 2024

Crossrefs

Cf. A007947, A020639, A065642, A120944, A126706, A364996, A364997, A364999.

Sequence in context: A051773 A307222 A336553 * A140278 A046426 A056776

Adjacent sequences: A366457 A366458 A366459 * A366461 A366462 A366463

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 05 2024

Status

approved