A349939 - OEIS

%I #15 Aug 14 2024 16:54:11

%S 187,245,275,403,425,427,437,473,583,605,637,665,731,763,775,805,845,

%T 847,875,893,931,1003,1075,1085,1127,1183,1235,1265,1267,1309,1357,

%U 1375,1397,1421,1435,1445,1463,1525,1547,1573,1577,1615,1625,1643,1645,1705,1757

%N Terms in A328897 that are not divisible by 3: numbers k > 1 not divisible by 2 or 3 such that A005179(k-1) > A005179(k) < A005179(k+1).

%C Numbers k not divisible by 2 or 3 such that, the smallest number with exactly k divisors is smaller than the smallest number with exactly k-1 or k+1 divisors.

%H Matthew House, <a href="/A349939/b349939.txt">Table of n, a(n) for n = 1..10000</a>

%e The smallest numbers with exactly 186, 187 and 188 divisors are 48318382080, 3869835264 and 1055531162664960 respectively. The smallest number with exactly 187 divisors is smaller than the smallest number with exactly 186 or 188 divisors, and 187 is not divisible by 2 or 3, so 187 is a term.

%e The smallest numbers with exactly 244, 245 and 246 divisors are 17293822569102704640, 29160000 and 49478023249920 respectively. The smallest number with exactly 245 divisors is smaller than the smallest number with exactly 244 or 246 divisors, and 245 is not divisible by 2 or 3, so 245 is a term.

%o (PARI) isA349939(k) = (k%2&&k%3&&k>1) && A005179(k)<A005179(k-1) && A005179(k)<A005179(k+1) \\ See A005179 for its program

%Y Cf. A005179, A328897, A349940.

%K nonn

%O 1,1

%A _Jianing Song_, Dec 05 2021