A252056 a(n) is the least m such that m = A001065(j) = A001065(k) where j != k, A000005(j) = A000005(k) = n; or 0 if no such m exists.

0, 1, 0, 13, 0, 73, 0, 106, 9064940, 4001, 0, 396, 0

Offset: 1

Author

Naohiro Nomoto, Dec 13 2014

Keywords

• nonn
• more

Comments

When n>2 and A001055(n)=1, then a(n)=0; because in that case, only a prime^n has n divisors, and then it is not possible to get twice the same value for sigma(x)-x. This happens for n=3, 5, 7, 11, 13, 17, 19, 23, 29, ... - Michel Marcus, Dec 16 2014

Note that for n=8, j and k do not have the same prime signature. - Michel Marcus, Dec 17 2014

Examples

			For n=2, all primes have 2 divisors and satisfy sigma(x)-x=1, so a(2) = 1.
For n=4, 27 and 35 have 4 divisors and the sum of their proper divisors is 13 for both (1+3+9 and 1+5+7).
For n=6, 98 and 175 have 6 divisors and the sum of their proper divisors is 73 for both (1+2+7+14+49 and 1+5+7+25+35).
For n=8, 104 and 110 have 8 divisors and the sum of their proper divisors is 106 for both (1+2+4+8+13+26+52 and 1+2+5+10+11+22+55).
For n=9, 163^2*167^2 and 61^2*353^2 have 9 divisors and the sum of their proper divisors is 9064940 for both.
For n=10, 7203 and 7857 have 10 divisors and the sum of their proper divisors is 4001 for both.
For n=12, 276 and 306 have 12 divisors and the sum of their proper divisors is 396 for both.
		

Crossrefs

Cf. A000005 (number of divisors of n), A001065 (sum of proper divisors of n).

Cf. A001055, A048138, A152454.

Extensions

a(9)-a(13) from Michel Marcus, Dec 16 2014