A353034 - OEIS

A353034

Numbers m such that tau(m) = 2 * tau(m + 1) and simultaneously sigma(m) = 2 * sigma(m + 1), where tau(k) = A000005(k) and sigma(k) = A000203(k).

%I #8 May 07 2022 10:40:02

%S 20118,20712,79338,103410,203898,267630,570342,907710,1093026,1228062,

%T 1263918,1663752,2322760,3268782,3468486,3527250,5483418,6277038,

%U 6500442,7637980,9181578,9297078,17708178,18638646,25274946,25364526,25768302,25909254,31118664

%N Numbers m such that tau(m) = 2 * tau(m + 1) and simultaneously sigma(m) = 2 * sigma(m + 1), where tau(k) = A000005(k) and sigma(k) = A000203(k).

%C Corresponding values of tau(m): 16, 16, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 32, ...

%C Corresponding values of sigma(m): 46080, 51840, 181440, 276480, 432000, 701568, 1200960, 2211840, ...

%e tau(20118) = 16 = 2 * tau(20119) = 2 * 8, sigma(20118) = 46080 = 2 * sigma(20119) = 2 * 23040.

%o (Magma) [m: m in [2..10^6] | #Divisors(m) eq 2 * #Divisors(m + 1) and &+Divisors(m) eq 2 * &+Divisors(m + 1)]

%Y Cf. A000005 (tau), A000203 (sigma), A054004, A347603, A353033.

%Y Subsequence of A163193.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Apr 18 2022