A073722 Least k such that sigma(k) mod primepi(k) = n or zero if no such number exists.

2, 4, 10, 8, 17, 42, 23, 111, 32, 59, 31, 67, 49, 110, 63, 60, 82, 84, 89, 75, 191, 98, 141, 97, 101, 256, 171, 169, 148, 144, 140, 159, 143, 222, 220, 172, 206, 2124, 183, 315, 263, 567, 201, 358, 204, 470, 243, 391, 264, 563, 295, 382, 290, 285, 313, 324, 307

Offset: 0

Author

Labos Elemer, Aug 05 2002

Keywords

• nonn

Examples

			n=8: a(8)=32 since sigma(32)=63, primepi(32)=11, and 63 mod 11 = 8.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000203, A000720, A072548, A073721-A073724.

Programs

Mathematica

t=Table[0, {100}]; Do[s=Mod[DivisorSigma[1, n], PrimePi[n]]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 2, 10000}]; t

Formula

a(n) = min{x: A000203(x) mod A000720(x) = n}.

Extensions

a(0)=2 inserted by Sean A. Irvine, Dec 16 2024