|
| |
|
|
A334794
|
|
a(n) = Sum_{d|n} lcm(sigma(d), pod(d)) where sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
|
|
1
|
|
|
|
1, 7, 13, 63, 31, 55, 57, 1023, 364, 937, 133, 12207, 183, 1239, 1843, 32767, 307, 76222, 381, 168993, 14181, 4495, 553, 1672047, 3906, 14385, 29524, 23247, 871, 812785, 993, 2097151, 17569, 31525, 58887, 917158710, 1407, 22047, 85371, 23209953, 1723, 6238791
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(p) = p^2 + p + 1 for p = primes (A000040).
|
|
|
EXAMPLE
|
a(6) = lcm(sigma(1), pod(1)) + lcm(sigma(2), pod(2)) + lcm(sigma(3), pod(3)) + lcm(sigma(6), pod(6)) = lcm(1, 1) + lcm(3, 2) + lcm(4, 3) + lcm(12, 36) = 1 + 6 + 12 + 36 = 55.
|
|
|
MATHEMATICA
|
a[n_] := DivisorSum[n, LCM[DivisorSigma[1, #], #^(DivisorSigma[0, #]/2)] &]; Array[a, 100] (* Amiram Eldar, May 12 2020 *)
|
|
|
PROG
|
(Magma) [&+[LCM(&+Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, lcm(sigma(d), vecprod(divisors(d)))); \\ Michel Marcus, May 12 2020
|
|
|
CROSSREFS
|
Cf. A334663 (Sum_{d|n} gcd(sigma(d), pod(d))), A334793 (Sum_{d|n} lcm(tau(d), pod(d))).
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
