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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Nov 19 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Bisection of A278260.

Cf. A002522, A046523.

Cf. A005574 (positions of 2's), A085722 (of 6's).

Cf. also A278160, A278244, A278254.

Programs

Mathematica

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 *)

PARI

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
A278162(n) = A046523((n^2)+1);
for(n=0, 10000, write("b278162.txt", n, " ", A278162(n)));

Scheme

(define (A278162 n) (A046523 (+ 1 (* n n))))

Formula

a(n) = A046523(A002522(n)) = A046523((n^2)+1).

a(n) = A278260(2*n).