OFFSET
1,1
COMMENTS
Numbers k such that A340388(k) is not the smallest number whose prime factors are all congruent to 1 modulo 4 and with exactly k divisors.
Despite being an analog of A072066, this sequence seems to be considerably sparser than A072066. What's the reason for that?
All powers of 2 that are greater than or equal to 16 are here. All numbers of the form 3 * 2^e with e >= 8 are here.
All powers of 3 that are greater than or equal to 3^15 = 14348907 are here. For example, we have A340388(3^15) = (5 * 13 * 17 * 29 * ... * 113 * 137)^2, while a(3^15) <= (5^4 * 13 * 17 * 29 * .. * 113)^2, so 3^15 is a term. Apparently 3^15 is the smallest odd term in this sequence.
Similarly, let q be a prime, then all powers of q that are greater than or equal to q^(N+1) are here, where N is the number of primes congruent to 1 modulo 4 below 5^q. It seems that q^(N+1) is the smallest q-rough term in this sequence.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Jianing Song, Apr 25 2021
STATUS
approved