A338395 Numbers m such that lcm(tau(m), sigma(m), pod(m)) = pod(m).

1, 6, 30, 66, 84, 102, 120, 210, 270, 318, 330, 420, 462, 510, 546, 570, 642, 672, 690, 714, 840, 870, 924, 930, 966, 1080, 1092, 1122, 1320, 1410, 1428, 1518, 1590, 1638, 1722, 1770, 1890, 1932, 2040, 2130, 2226, 2280, 2310, 2346, 2370, 2604, 2670, 2730, 2760

Offset: 1

Author

Jaroslav Krizek, Oct 23 2020

Keywords

• nonn

Comments

Numbers m such that A336723(m)= lcm(A000005(m), A000203(m), A007955(m)) = A007955(m).

Numbers m such that both values tau(m) and sigma(m) divide pod(m).

Numbers m such that all values m, tau(m) and sigma(m) divide pod(m); i.e. lcm(m, tau(m), sigma(m), pod(m)) = pod(m).

Supersequence of A277521.

Examples

			lcm(tau(6), sigma(6), pod(6)) = lcm(4, 12, 36) = 36 = pod(6).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..12916 (a(n) < 10^7)
• Vaclav Kotesovec, Plot of a(n)/n^(3/2) for n = 1..12916

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A007955 (pod).

Cf. A277521, A336723.

Programs

Magma

[m: m in [1..10^5] | LCM([#Divisors(m), &+Divisors(m), &*Divisors(m)]) eq &*Divisors(m)]

Mathematica

Select[Range[3000], LCM @@ {(d = DivisorSigma[0, #]), DivisorSigma[1, #], (pod = #^(d/2))} == pod &] (* Amiram Eldar, Oct 24 2020 *)

PARI

isok(m) = my(d=divisors(m), prd=vecprod(d)); lcm([#d, vecsum(d), prd]) == prd; \\ Michel Marcus, Oct 24 2020