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A308710 Primitive practical numbers of the form 2^i * prime(k). 1
6, 20, 28, 88, 104, 272, 304, 368, 464, 496, 1184, 1312, 1376, 1504, 1696, 1888, 1952, 4288, 4544, 4672, 5056, 5312, 5696, 6208, 6464, 6592, 6848, 6976, 7232, 8128, 16768, 17536, 17792, 19072, 19328, 20096, 20864, 21376, 22144, 22912, 23168, 24448, 24704, 25216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A267124 and A100368.

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

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

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

MATHEMATICA

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

PROG

(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

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

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

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

isok(n) = isppt(n) && ispp(n); \\ Michel Marcus, Jun 19 2019

CROSSREFS

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

Sequence in context: A180332 A064771 A006036 * A242341 A140738 A325593

Adjacent sequences:  A308707 A308708 A308709 * A308711 A308712 A308713

KEYWORD

nonn

AUTHOR

Miko Labalan, Jun 19 2019

STATUS

approved

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Last modified February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)