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A178740 Product of the 5th power of a prime (A050997) and a different prime (p^5*q). 9

%I

%S 96,160,224,352,416,486,544,608,736,928,992,1184,1215,1312,1376,1504,

%T 1696,1701,1888,1952,2144,2272,2336,2528,2656,2673,2848,3104,3159,

%U 3232,3296,3424,3488,3616,4064,4131,4192,4384,4448,4617,4768,4832,5024,5216

%N Product of the 5th power of a prime (A050997) and a different prime (p^5*q).

%C Subsequence of A030630, integers whose number of divisors is 12. - _Michel Marcus_, Nov 11 2015

%H T. D. Noe, <a href="/A178740/b178740.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>

%F Solutions of the equation tau(n^5)=13*tau(n) where tau(n) is the number of divisors of n. - _Paolo P. Lava_, Mar 15 2013

%p with(numtheory);

%p A178740:=proc(q) local n;

%p for n from 1 to q do if tau(n^5)=13*tau(n) then print(n); fi; od; end:

%p A178740(10^10); # _Paolo P. Lava_, Mar 15 2013

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,5};Select[Range[6000],f] (* _Vladimir Joseph Stephan Orlovsky_, May 03 2011 *)

%t With[{nn=50},Take[Union[Flatten[{#[[1]]^5 #[[2]],#[[1]]#[[2]]^5}&/@Subsets[ Prime[ Range[nn]],{2}]]],nn]] (* _Harvey P. Dale_, Mar 18 2013 *)

%o (PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\2)^(1/5), t=p^5; forprime(q=2, lim\t, if(p==q, next); listput(v, t*q))); vecsort(Vec(v)) \\ _Altug Alkan_, Nov 11 2015

%o (PARI) isok(n)=my(f=factor(n)[, 2]); f==[5, 1]~||f==[1, 5]~

%o for(n=1, 1e4, if(isok(n), print1(n,", "))) \\ _Altug Alkan_, Nov 11 2015

%Y Cf. A178739, A050997 and A143610.

%K easy,nonn

%O 1,1

%A _Will Nicholes_, Jun 08 2010

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Last modified April 16 21:58 EDT 2021. Contains 343051 sequences. (Running on oeis4.)