cp's OEIS Frontend

A276936 Numbers m with at least one distinct prime factor prime(k) such that prime(k)^k divides, but prime(k)^(k+1) does not divide m.

%I A276936 #25 Nov 18 2024 06:25:36
%S A276936 2,6,9,10,14,18,22,26,30,34,36,38,42,45,46,50,54,58,62,63,66,70,72,74,
%T A276936 78,82,86,90,94,98,99,102,106,110,114,117,118,122,125,126,130,134,138,
%U A276936 142,144,146,150,153,154,158,162,166,170,171,174,178,180,182,186,190,194,198,202,206,207,210,214,218,222,225
%N A276936 Numbers m with at least one distinct prime factor prime(k) such that prime(k)^k divides, but prime(k)^(k+1) does not divide m.
%C A276936 Numbers m with at least one prime factor such that the exponent of its highest power in m is equal to the index of that prime.
%C A276936 The asymptotic density of this sequence is 1 - Product_{k>=1} (1 - 1/prime(k)^k + 1/prime(k)^(k+1)) = 0.31025035294364447031... - _Amiram Eldar_, Jan 09 2021
%H A276936 Amiram Eldar, <a href="/A276936/b276936.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5500 from Antti Karttunen)
%e A276936 2 is a member as 2 = prime(1) and as 2^1 divides but 2^2 does not divide 2.
%e A276936 3 is NOT a member as 3 = prime(2) but 3^2 does not divide 3.
%e A276936 4 is NOT a member as 2^2 divides 4.
%e A276936 6 is a member as 2 = prime(1) and 2^1 is a divisor of 6, but 2^2 is not.
%e A276936 9 is a member as 3 = prime(2) and 3^2 divides 9.
%p A276936 q:= n-> ormap(i-> numtheory[pi](i[1])=i[2], ifactors(n)[2]):
%p A276936 select(q, [$1..225])[];  # _Alois P. Heinz_, Nov 18 2024
%t A276936 Select[Range[225], AnyTrue[FactorInteger[#], PrimePi[First[#1]] == Last[#1] &] &] (* _Amiram Eldar_, Jan 09 2021 *)
%o A276936 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A276936 (define A276936 (NONZERO-POS 1 1 A276935))
%Y A276936 Cf. A109298, A276935.
%Y A276936 Intersection with A276078 gives A276937.
%Y A276936 Cf. A016825, A051063 (subsequences).
%Y A276936 Complement of A325130.
%K A276936 nonn
%O A276936 1,1
%A A276936 _Antti Karttunen_, Sep 24 2016