A278160 -id:A278160 - cp's OEIS frontend

A278254 Least number with the prime signature of n^2; square of the least number with the prime signature of n.

1, 4, 4, 16, 4, 36, 4, 64, 16, 36, 4, 144, 4, 36, 36, 256, 4, 144, 4, 144, 36, 36, 4, 576, 16, 36, 64, 144, 4, 900, 4, 1024, 36, 36, 36, 1296, 4, 36, 36, 576, 4, 900, 4, 144, 144, 36, 4, 2304, 16, 144, 36, 144, 4, 576, 36, 576, 36, 36, 4, 3600, 4, 36, 144, 4096, 36, 900, 4, 144, 36, 900, 4, 5184, 4, 36, 144, 144, 36, 900, 4, 2304, 256, 36, 4, 3600, 36, 36, 36

Offset: 1

Antti Karttunen, Nov 19 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Bisection of A278259.

Cf. A000290, A046523, A278238, A278253, A278160, A278162.

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

a(n)=my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i])^2 \\ Charles R Greathouse IV, Feb 03 2017

(define (A278254 n) (A000290 (A046523 n)))
(define (A278254 n) (A046523 (A000290 n)))

a(n) = A046523(n^2) = A046523(n)^2.

a(n) = A278259(2*n).

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

Original entry on oeis.org

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

Antti Karttunen, Nov 19 2016

nonn

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

Bisection of A278260.
Cf. A002522, A046523.
Cf. A005574 (positions of 2's), A085722 (of 6's).
Cf. also A278160, A278244, A278254.

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 *)

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)));

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

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

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

A278497 a(n) = Least number with the prime signature of A276573(n).

Original entry on oeis.org

2, 6, 8, 2, 6, 16, 12, 6, 24, 8, 30, 32, 6, 6, 24, 2, 12, 48, 6, 2, 24, 2, 12, 64, 2, 30, 72, 12, 30, 48, 2, 6, 24, 60, 6, 96, 12, 30, 30, 72, 48, 6, 12, 120, 6, 60, 128, 2, 6, 24, 2, 6, 144, 12, 2, 24, 6, 6, 96, 48, 30, 120, 12, 2, 48, 2, 6, 30, 24, 192, 30, 60, 72, 6, 12, 210, 6, 216, 6, 6, 96, 2, 30, 2, 12, 240, 32, 12, 24, 2, 30, 256, 6, 12, 120, 6, 120

Offset: 1

Antti Karttunen, Nov 25 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10028

Cf. A002828, A046523, A260733, A276573, A278160, A278498, A278499.
Cf. A277014 (gives the indices of squares).
Cf. also A278232.

(define (A278497 n) (A046523 (A276573 n)))

a(n) = A046523(A276573(n)).

For all n >= 1, a(A260733(1+n)) = A278160(n).

cp's OEIS Frontend

A278254 Least number with the prime signature of n^2; square of the least number with the prime signature of n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Scheme

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Scheme

Formula

A278497 a(n) = Least number with the prime signature of A276573(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula