A278256 -id:A278256 - cp's OEIS frontend

A278253 Least number with the prime signature of the n-th triangular number.

1, 2, 6, 6, 6, 6, 12, 36, 12, 6, 30, 30, 6, 30, 120, 24, 12, 12, 30, 210, 30, 6, 60, 180, 12, 24, 120, 30, 30, 30, 48, 240, 30, 30, 420, 60, 6, 30, 420, 60, 30, 30, 30, 420, 60, 6, 120, 360, 36, 60, 210, 30, 24, 120, 420, 420, 30, 6, 210, 210, 6, 60, 1440, 480, 210, 30, 30, 210, 210, 30, 180, 180, 6, 60, 420, 210, 210, 30, 120, 2160, 48, 6, 210, 2310, 30, 30

Offset: 1

Antti Karttunen, Nov 19 2016

nonn

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

Cf. A000217, A046523, A278254, A278256.

Diagonal 2 of triangle A278218.

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ (n^2 - n)/2], {n, 2, 87}] (* Michael De Vlieger, Nov 21 2016 *)

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

(define (A278253 n) (A046523 (A000217 n)))

a(n) = A046523(A000217(n)).

A278259 Least number with the prime signature of the n-th quarter-square, a(1) = 0.

Original entry on oeis.org

0, 1, 2, 4, 6, 4, 12, 16, 12, 4, 30, 36, 30, 4, 24, 64, 72, 16, 60, 36, 30, 4, 60, 144, 60, 4, 30, 36, 210, 36, 240, 256, 48, 4, 60, 144, 60, 4, 60, 144, 420, 36, 210, 36, 30, 4, 120, 576, 360, 16, 60, 36, 120, 64, 360, 144, 60, 4, 210, 900, 210, 4, 96, 1024, 480, 36, 210, 36, 210, 36, 1260, 1296, 180, 4, 30, 36, 210, 36, 840, 576, 120, 4, 210, 900, 210, 4, 60

Offset: 1

Antti Karttunen, Nov 22 2016

nonn

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

Cf. A002620, A046523.
Cf. A278254, A278256 (bisections).
Cf. also A278260.

(define (A278259 n) (if (<= n 1) 0 (A046523 (A002620 n))))

a(1) = 0; for n > 1, a(n) = A046523(A002620(n)).

cp's OEIS Frontend

A278253 Least number with the prime signature of the n-th triangular number.

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