A294393 a(n) is the smallest number whose deficiency or abundance is equal to 2*n (or 0 if such a number does not exist), minus the n-th odd number.

5, 0, 0, 0, 13, 0, 0, 12, 0, 0, 25, 0, 87, 31, 0, 0, 217, 22, 0, 16, 0, 0, 49, 0, 11, 55, 0, 32, 27, 0, 0, 22, 43, 0, 73, 0, 0, 637, 81, 0, 75, 0, 320, 28, 0, 50, 313, 24, 0, 103, 0, 0, 109, 0, 0, 34, 0, 62, 301, 24, -1, 120, 67, 0, 133, 0, 128, 139, 0, 0, 433, 42, 23, 151, 0, 0, 219, 82, 0, 28, 119

Offset: 0

Author

Omar E. Pol, Oct 30 2017

Keywords

• sign

Comments

Note that a(60) = -1.

Examples

			--------------------------------------
n    A294386(n) - A005408(n)  =  a(n)
--------------------------------------
0        6            1           5
1        3            3           0
2        5            5           0
3        7            7           0
4       22            9          13
...
		

Crossrefs

Cf. A000203, A000396, A005100, A005101, A033879, A033880, A234285, A234286, A294347, A294386.

Programs

PARI

f(n) = abs(2*n-sigma(n));
a(n) = my(k=1); while(f(k) != 2*n, k++); k - (2*n+1); \\ Michel Marcus, Oct 31 2017

Formula

a(n) = A294386(n) - A005408(n).