cp's OEIS Frontend

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

%I A354357 #11 Dec 17 2023 14:04:53
%S A354357 1,5,7,11,17,23,31,35,47,53,55,71,77,85,107,115,119,127,155,161,187,
%T A354357 191,217,235,253,265,329,341,355,371,383,385,391,431,497,517,527,535,
%U A354357 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
%N A354357 Numbers k, not divisible by 2 or 3, such that sigma(k) is 3-smooth (has no larger prime factors than 3).
%H A354357 Amiram Eldar, <a href="/A354357/b354357.txt">Table of n, a(n) for n = 1..10000</a>
%t A354357 Select[Flatten @ Outer[Plus, 6 * Range[0, 300], {1, 5}], Max @ FactorInteger[DivisorSigma[1, #]][[;;, 1]] <= 3 &] (* _Amiram Eldar_, May 25 2022 *)
%t A354357 Select[Range[1,1701,2],Mod[#,3]!=0&&Max[FactorInteger[DivisorSigma[1,#]][[;;,1]]]<4&] (* _Harvey P. Dale_, Dec 17 2023 *)
%o A354357 (PARI)
%o A354357 A065333(n) = ((3^valuation(n, 3)<<valuation(n, 2))==n); \\ From A065333
%o A354357 A354355(n) = A065333(sigma(n));
%o A354357 isA354357(n) = ((n%2)&&(n%3)&&A354355(n));
%Y A354357 Intersection of A007310 and A354356.
%Y A354357 Sequence A354202(A354361(n)), n>=1, sorted into ascending order.
%Y A354357 Cf. A000203, A065333.
%K A354357 nonn
%O A354357 1,2
%A A354357 _Antti Karttunen_, May 24 2022