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 A308710 Primitive practical numbers of the form 2^i * prime(k). 1

%I

%S 6,20,28,88,104,272,304,368,464,496,1184,1312,1376,1504,1696,1888,

%T 1952,4288,4544,4672,5056,5312,5696,6208,6464,6592,6848,6976,7232,

%U 8128,16768,17536,17792,19072,19328,20096,20864,21376,22144,22912,23168,24448,24704,25216

%N Primitive practical numbers of the form 2^i * prime(k).

%C Intersection of A267124 and A100368.

%C a(n) is a number of the form 2^i * prime(k) for i > 0 and A007053(i) < k <= A007053(i+1).

%C Terms are pseudoperfect numbers, A005835 and are also primitive pseudoperfect numbers, A006036.

%H Amiram Eldar, <a href="/A308710/b308710.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2^floor(log_2(prime(n+1))) * prime(n+1).

%t a[n_] := (p = Prime[n+1]) * 2^Floor[Log2[p]]; Array[a, 50] (* _Amiram Eldar_, Sep 22 2019 *)

%o (PARI) ispract(n) = bittest(n, 0) && return(n==1); my(P=1); n && !for(i=2, #n=factor(n)~, n[1, i]>1+(P*=sigma(n[1, i-1]^n[2, i-1])) && return); \\ A005153

%o isp(n) = {my(f=factor(n)); for (k=1, #f~, if ((f[k,2] > 1) && ispract(n/f[k,1]), return (0));); return (1);}

%o ispp(n) = ispract(n) && (issquarefree(n) || isp(n)); \\ A267124

%o isppt(n) = (n%2==0) && isprime(n>>valuation(n, 2)); \\ A100368

%o isok(n) = isppt(n) && ispp(n); \\ _Michel Marcus_, Jun 19 2019

%Y Cf. A000040, A000079, A005153, A005835, A006036, A007053, A100368, A267124.

%K nonn

%O 1,1

%A _Miko Labalan_, Jun 19 2019

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)