cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A144671 Numbers n such that omega(n) = omega(2^n-1), where omega = A001221 = number of distinct prime factors.

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%I A144671 #7 Jan 04 2018 18:33:21
%S A144671 1,2,3,5,6,7,13,17,19,31,61,89,107,127,521,607
%N A144671 Numbers n such that omega(n) = omega(2^n-1), where omega = A001221 = number of distinct prime factors.
%C A144671 A prime p is in this sequence iff 2^p-1 is prime, thus iff p is in A000043 (Mersenne prime exponents), which is a subsequence of this one - and of A155990. The latter contains (some) powers of primes, which cannot be the case here.
%e A144671 a(1) = 1 is in this sequence since omega(1) = 0 = omega(2^1-1). Elements of A000043 are primes p such that 2^p-1, they are in this sequence since omega(p) = 1 = omega(2^p-1). a(5) = 6 is in this sequence since omega(6) = #{2,3} = 2 = omega(2^6-1) = #{3,7}.
%t A144671 Select[Range[700],PrimeNu[#]==PrimeNu[2^#-1]&] (* _Harvey P. Dale_, Jan 04 2018 *)
%o A144671 (PARI) is_A144671(n)={ omega(n)==omega(2^n-1) }
%K A144671 more,nonn
%O A144671 1,2
%A A144671 _M. F. Hasler_, Feb 01 2009
%E A144671 Two more terms from _Max Alekseyev_, Apr 27 2010