cp's OEIS Frontend

A278162 Least number with the prime signature of n^2 + 1.

%I A278162 #23 Nov 22 2016 21:47:42
%S A278162 1,2,2,6,2,6,2,12,6,6,2,6,6,30,2,6,2,30,12,6,2,30,6,30,2,6,2,30,6,6,6,
%T A278162 30,12,30,6,6,2,30,12,6,2,12,6,60,6,6,6,210,6,6,6,6,6,30,2,30,2,120,6,
%U A278162 6,6,6,6,30,6,6,2,30,24,6,12,6,30,210,2,30,6,30,6,6,6,30,12,210,2,6,6,30,6,30,2,30,6,60,2,6,6,30,30,60,6,6,6,30,6,30,6
%N A278162 Least number with the prime signature of n^2 + 1.
%H A278162 Antti Karttunen, <a href="/A278162/b278162.txt">Table of n, a(n) for n = 0..10000</a>
%F A278162 a(n) = A046523(A002522(n)) = A046523((n^2)+1).
%F A278162 a(n) = A278260(2*n).
%t A278162 Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ n^2 + 1], {n, 0, 120}] (* _Michael De Vlieger_, Nov 21 2016 *)
%o A278162 (PARI)
%o A278162 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 A278162 A278162(n) = A046523((n^2)+1);
%o A278162 for(n=0, 10000, write("b278162.txt", n, " ", A278162(n)));
%o A278162 (Scheme) (define (A278162 n) (A046523 (+ 1 (* n n))))
%Y A278162 Bisection of A278260.
%Y A278162 Cf. A002522, A046523.
%Y A278162 Cf. A005574 (positions of 2's), A085722 (of 6's).
%Y A278162 Cf. also A278160, A278244, A278254.
%K A278162 nonn
%O A278162 0,2
%A A278162 _Antti Karttunen_, Nov 19 2016