A329525 a(n) is the smallest positive number k such that k and k+n are both abundant.

5775, 18, 942, 20, 940, 12, 945, 12, 936, 20, 4725, 12, 4712, 40, 930, 20, 928, 12, 2816, 20, 924, 18, 945, 12, 920, 30, 918, 12, 2176, 12, 3465, 24, 912, 20, 910, 12, 7208, 18, 906, 20, 4095, 12, 5312, 12, 900, 20, 945, 12, 896, 20, 894, 18, 4672, 12, 945, 24

Offset: 1

Author

Jaroslav Krizek, Nov 15 2019

Keywords

• nonn

Comments

Sequences of numbers k such that k and k+n are both abundant for any n: A096399 (n = 1), A231086 (n = 2).

Examples

			Number 5775 is the smallest abundant number k such that k+1 = 5576 is also abundant.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A005101, A096399, A231086, A294937.

Programs

Magma

[Min([m: m in[1..10^4] | SumOfDivisors(m) gt 2*m and SumOfDivisors(m+n) gt 2*(m+n)]): n in [1..60]];

PARI

A329525(n) = for(k=1, oo, if((sigma(k) > (k+k)) && (sigma(n+k) > 2*(n+k)), return(k))); \\ Antti Karttunen, Nov 15 2019