A354357 Numbers k, not divisible by 2 or 3, such that sigma(k) is 3-smooth (has no larger prime factors than 3).

1, 5, 7, 11, 17, 23, 31, 35, 47, 53, 55, 71, 77, 85, 107, 115, 119, 127, 155, 161, 187, 191, 217, 235, 253, 265, 329, 341, 355, 371, 383, 385, 391, 431, 497, 517, 527, 535, 583, 595, 635, 647, 713, 749, 781, 799, 805, 863, 889, 901, 935, 955, 971, 1081, 1085, 1151, 1177, 1207, 1219, 1265, 1309, 1337, 1397, 1457, 1633

Offset: 1

Author

Antti Karttunen, May 24 2022

Keywords

• nonn

Links

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

Crossrefs

Intersection of A007310 and A354356.

Sequence A354202(A354361(n)), n>=1, sorted into ascending order.

Cf. A000203, A065333.

Programs

Mathematica

Select[Flatten @ Outer[Plus, 6 * Range[0, 300], {1, 5}], Max @ FactorInteger[DivisorSigma[1, #]][[;;, 1]] <= 3 &] (* Amiram Eldar, May 25 2022 *)
Select[Range[1,1701,2],Mod[#,3]!=0&&Max[FactorInteger[DivisorSigma[1,#]][[;;,1]]]<4&] (* Harvey P. Dale, Dec 17 2023 *)

PARI

A065333(n) = ((3^valuation(n, 3)<A065333
A354355(n) = A065333(sigma(n));
isA354357(n) = ((n%2)&&(n%3)&&A354355(n));