A278246 a(n) = least number with the same prime signature as n*(n+3)/2.

2, 2, 4, 6, 12, 8, 6, 12, 24, 6, 6, 60, 24, 6, 24, 24, 30, 24, 6, 30, 180, 12, 6, 144, 60, 6, 48, 30, 48, 60, 6, 240, 120, 6, 30, 120, 60, 6, 60, 60, 30, 120, 6, 30, 1080, 12, 12, 360, 60, 12, 48, 210, 60, 48, 30, 60, 420, 6, 6, 840, 96, 30, 120, 96, 210, 60, 30, 30, 360, 30, 6, 1800, 30, 30, 180, 30, 840, 96, 6, 120, 480, 30, 6, 420, 420, 6, 120, 420, 30, 120

Offset: 1

Author

Antti Karttunen, Nov 21 2016

Keywords

• nonn

Comments

For n > 2, 6 <= a(n) <= n*(n+3)/2. The upper bound occurs for n = 1, 45, 165, 525, 672, 1152, and no others up to 10^9. (Probably this occurs only finitely many times.) - Charles R Greathouse IV, Nov 23 2016

Links

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

Crossrefs

Cf. A000096, A046523, A278247, A278251, A278253, A278255.

Programs

PARI

A046523(n)=my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i])
a(n)=A046523(n*(n+3)/2) \\ Charles R Greathouse IV, Nov 21 2016

Scheme

(define (A278246 n) (A046523 (A000096 n)))

Formula

a(n) = A046523(A000096(n)).