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A031126 Number of proper factorizations of p1^n*p2^3, where p1 and p2 are distinct primes. 1

%I #11 May 01 2017 13:11:59

%S 2,6,15,30,56,96,161,256,400,607,906,1324,1913,2718,3823,5312,7315,

%T 9972,13494,18104,24131,31937,42020,54947,71483,92491,119119,152685,

%U 194886,247692,313612,395546,497153,622687,777423,967524,1200571

%N Number of proper factorizations of p1^n*p2^3, where p1 and p2 are distinct primes.

%H Ray Chandler, <a href="/A031126/b031126.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A000412(n) - 1 = A028422(2^n*3^3). - _Ray Chandler_, May 01 2017

%e a(0)=2 since 2^3=8 has two proper (i.e. nontrivial) factorizations, 2*4 and 2*2*2. a(1)=6 since 2*3^3 = 54 has the proper factorizations 2*27, 2*3*9, 2*3*3*3, 6*3*3, 6*9, 18*3. - _N. J. A. Sloane_, May 01 2017

%Y Cf. A000412, A028422.

%K nonn

%O 0,1

%A _Jeff Burch_

%E Offset changed to 0 and more terms added by _Ray Chandler_, May 01 2017

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Last modified April 27 23:22 EDT 2024. Contains 372020 sequences. (Running on oeis4.)