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Numbers divisible by exactly one odd prime.
12

%I #40 May 22 2024 12:55:06

%S 3,5,6,7,9,10,11,12,13,14,17,18,19,20,22,23,24,25,26,27,28,29,31,34,

%T 36,37,38,40,41,43,44,46,47,48,49,50,52,53,54,56,58,59,61,62,67,68,71,

%U 72,73,74,76,79,80,81,82,83,86,88,89,92,94,96,97,98,100,101,103,104

%N Numbers divisible by exactly one odd prime.

%C Numbers k for which A001221(A000265(k)) = 1. - _Antti Karttunen_, Jul 08 2020

%C Numbers whose odd part is a prime power (A246655). - _Amiram Eldar_, Jul 08 2020

%C Numbers of the form 2^r * p^q with p an odd prime (A065091), r >= 0, q >= 1. - _Bernard Schott_, Dec 14 2020

%H Amiram Eldar, <a href="/A336101/b336101.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[104], PrimePowerQ[#/2^IntegerExponent[#, 2]] &] (* _Amiram Eldar_, Jul 08 2020 *)

%o (PARI) isA336101(n) = (1==omega(n>>valuation(n,2))); \\ _Antti Karttunen_, Jul 08 2020

%Y Cf. A000265, A001221, A246655, A340373 (characteristic function).

%Y Positions of ones in A005087.

%Y Subsequence of A267895.

%Y Subsequences: A007283 (3*2^n), A020714 (5*2^n), A005009 (7*2^n), A005015 (11*2^n), A005029 (13*2^n), A038550 (p*2^n, p odd prime), A065091 (odd primes), A061345 \ {1} (odd prime powers).

%K nonn,easy

%O 1,1

%A _Peter Munn_, Jul 08 2020