A278240 -id:A278240 - cp's OEIS frontend

A278160 Least number with the prime signature of ((n+1)^2 - 1).

2, 8, 6, 24, 6, 48, 12, 48, 12, 120, 6, 120, 30, 96, 30, 288, 6, 360, 30, 120, 30, 240, 12, 240, 72, 120, 24, 840, 6, 960, 30, 192, 210, 360, 30, 360, 30, 240, 30, 1680, 6, 840, 60, 120, 60, 480, 12, 1440, 60, 360, 30, 1080, 30, 2160, 210, 240, 30, 840, 6, 840, 60, 384, 420, 1920, 30, 840, 30, 840, 30, 5040, 6, 720, 60, 120, 420, 840, 30, 3360, 48, 480, 48

Offset: 1

Antti Karttunen, Nov 19 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1024

Cf. A005563, A046523.
Cf. A001359 (positions of 6's).
Cf. also A278240, A278242, A278253, A278254, A278162.

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ (n + 1)^2 - 1], {n, 120}] (* Michael De Vlieger, Nov 21 2016 *)

(define (A278160 n) (A046523 (A005563 n)))
(define (A005563 n) (* n (+ 2 n)))

a(n) = A046523(A005563(n)) = A046523(((n+1)^2)-1).

A278242 Least number with the prime signature of 2^n + 1.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Nov 19 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..257

Cf. A000051, A046523.
Cf. A073936 (positions of 6's), A092559 (positions of 4's and 6's).
Cf. also A278240.

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ 2^n + 1], {n, 0, 80}] (* Michael De Vlieger, Nov 21 2016 *)

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
A278242(n) = A046523((2^n)+1);
for(n=0, 257, write("b278242.txt", n, " ", A278242(n)));

(define (A278242 n) (A046523 (A000051 n)))

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

cp's OEIS Frontend

A278160 Least number with the prime signature of ((n+1)^2 - 1).

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