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, 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

Offset: 1

Author

Jaroslav Krizek, May 12 2020

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A334663 (Sum_{d|n} gcd(sigma(d), pod(d))), A334793 (Sum_{d|n} lcm(tau(d), pod(d))).

Cf. A000203 (sigma(n)), A007955 (pod(n)), A324529 (lcm(sigma(n), pod(n))).

Programs

Magma

[&+[LCM(&+Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]]

Mathematica

a[n_] := DivisorSum[n, LCM[DivisorSigma[1, #], #^(DivisorSigma[0, #]/2)] &]; Array[a, 100] (* Amiram Eldar, May 12 2020 *)

PARI

a(n) = sumdiv(n, d, lcm(sigma(d), vecprod(divisors(d)))); \\ Michel Marcus, May 12 2020

Formula

a(p) = p^2 + p + 1 for p = primes (A000040).