A325029 a(n) = Sum_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).

1, 7, 13, 63, 31, 451, 57, 1023, 364, 1837, 133, 48891, 183, 4767, 5443, 32767, 307, 228250, 381, 337893, 14181, 17563, 553, 19956411, 3906, 28581, 29524, 1234135, 871, 58327681, 993, 2097151, 52417, 62737, 58887, 917347026, 1407, 87027, 85371, 230738853, 1723

Offset: 1

Author

Jaroslav Krizek, Apr 25 2019

Keywords

• nonn

Comments

n divides a(n) for n = 1, 39, 793, 2800, 5289, 6601, 15747, 41041, ...

Examples

			a(6) = sigma(1)*pod(1) + sigma(2)*pod(2) + sigma(3)*pod(3) + sigma(6)*pod(6) = (1*1) + (3*2) + (4*3) + (12*36) = 451.
		

Crossrefs

Cf. A000203, A007955, A325030.

Programs

Magma

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

PARI

a(n) = sumdiv(n, d, my(dd=divisors(d)); vecsum(dd)*vecprod(dd)); \\ Michel Marcus, Apr 25 2019

Formula

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