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Numbers of the form prime(x) * prime(y) where x divides y.
20

%I #11 Nov 04 2022 19:24:39

%S 4,6,9,10,14,21,22,25,26,34,38,39,46,49,57,58,62,65,74,82,86,87,94,

%T 106,111,115,118,121,122,129,133,134,142,146,158,159,166,169,178,183,

%U 185,194,202,206,213,214,218,226,235,237,254,259,262,267,274,278,289

%N Numbers of the form prime(x) * prime(y) where x divides y.

%H Andrew Howroyd, <a href="/A318990/b318990.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of all dividing pairs (columns) begins:

%e 1 1 2 1 1 2 1 3 1 1 1 2 1 4 2 1 1 3 1 1 1 2 1 1

%e 1 2 2 3 4 4 5 3 6 7 8 6 9 4 8 10 11 6 12 13 14 10 15 16

%t Select[Range[100],And[PrimeOmega[#]==2,Or[PrimePowerQ[#],Divisible@@Reverse[PrimePi/@FactorInteger[#][[All,1]]]]]&]

%o (PARI) ok(n)={my(f=factor(n)); bigomega(f)==2 && (#f~==1 || primepi(f[2,1]) % primepi(f[1,1]) == 0)} \\ _Andrew Howroyd_, Oct 26 2018

%Y A subset of A001358 (semiprimes), squarefree A006881.

%Y The squarefree version is A339005.

%Y The quotient is A358103 = A358104 / A358105.

%Y A000040 lists the primes.

%Y A001222 counts prime indices, distinct A001221.

%Y A003963 multiplies together prime indices.

%Y A056239 adds up prime indices.

%Y A358192/A358193 gives quotients of semiprime indices.

%Y Cf. A000837, A300912, A318991, A318992, A318993.

%Y Cf. A000720, A027751, A032741, A215366, A296150.

%Y Cf. A289508, A289509, A358106.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 06 2018