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Least number with the prime signature of 2^n + 1.
3

%I #19 Nov 22 2016 21:49:17

%S 2,2,2,4,2,6,6,6,2,24,12,6,6,6,30,60,2,6,210,6,6,60,30,6,30,210,210,

%T 240,6,30,4620,6,6,420,210,2310,210,30,210,60,6,30,30030,6,30,9240,

%U 2310,30,30,30,9240,4620,30,30,30030,4620,30,420,30,210,210,6,2310,9240,6,30030,30030,30,60,420,60060,30,2310,30,2310,60060,210,30030,446185740,6,30

%N Least number with the prime signature of 2^n + 1.

%H Antti Karttunen, <a href="/A278242/b278242.txt">Table of n, a(n) for n = 0..257</a>

%F a(n) = A046523(A000051(n)).

%t Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]] &@ FactorInteger[ 2^n + 1], {n, 77}] (* _Michael De Vlieger_, Nov 21 2016 *)

%o (PARI)

%o A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ from _Charles R Greathouse IV_, Aug 17 2011

%o A278242(n) = A046523((2^n)+1);

%o for(n=0, 257, write("b278242.txt", n, " ", A278242(n)));

%o (Scheme) (define (A278242 n) (A046523 (A000051 n)))

%Y Cf. A000051, A046523.

%Y Cf. A073936 (positions of 6's), A092559 (positions of 4's and 6's).

%Y Cf. also A278240.

%K nonn

%O 0,1

%A _Antti Karttunen_, Nov 19 2016