cp's OEIS Frontend

A276079 Numbers n such that prime(k)^(k+1) divides n for some k.

%I A276079 #20 Apr 30 2021 12:39:06
%S A276079 4,8,12,16,20,24,27,28,32,36,40,44,48,52,54,56,60,64,68,72,76,80,81,
%T A276079 84,88,92,96,100,104,108,112,116,120,124,128,132,135,136,140,144,148,
%U A276079 152,156,160,162,164,168,172,176,180,184,188,189,192,196,200,204,208,212,216,220,224,228,232,236,240,243,244,248,252,256,260,264,268,270,272
%N A276079 Numbers n such that prime(k)^(k+1) divides n for some k.
%C A276079 The asymptotic density of this sequence is 1 - Product_{i>=1} 1-prime(i)^(-1-i) = 0.2789766... - _Amiram Eldar_, Oct 21 2020
%H A276079 Antti Karttunen, <a href="/A276079/b276079.txt">Table of n, a(n) for n = 1..5000</a>
%e A276079 625 = 5*5*5*5 = prime(3)^4 so it is divisible by prime(3)^(3+1), and thus 625 is included in the sequence.
%o A276079 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A276079 (define A276079 (NONZERO-POS 1 1 A276077))
%o A276079 (Python)
%o A276079 from sympy import primepi, isprime, primefactors, factorint
%o A276079 def a028234(n):
%o A276079     f=factorint(n)
%o A276079     minf = min(f)
%o A276079     return 1 if n==1 else n//(minf**f[minf])
%o A276079 def a067029(n):
%o A276079     f=factorint(n)
%o A276079     return 0 if n==1 else f[min(f)]
%o A276079 def a049084(n): return primepi(n) if isprime(n) else 0
%o A276079 def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
%o A276079 def a(n): return 0 if n==1 else a(a028234(n)) + (1 if a067029(n) > a055396(n) else 0)
%o A276079 print([n for n in range(1, 301) if a(n)!=0]) # _Indranil Ghosh_, Jun 21 2017
%Y A276079 Positions of nonzeros in A276077.
%Y A276079 Complement: A276078.
%Y A276079 Cf. A000040, A000720, A008586 (a subsequence).
%Y A276079 Differs from its subsequence A100716 for the first time at n=175, where a(175) = 625, while that value is missing from A100716.
%K A276079 nonn
%O A276079 1,1
%A A276079 _Antti Karttunen_, Aug 18 2016