A385705 Primes p such that there exists prime q < p such that sigma(p+1)=sigma(q+1).

37, 61, 109, 139, 157, 181, 193, 233, 269, 283, 347, 349, 353, 367, 373, 379, 487, 521, 541, 563, 571, 593, 613, 617, 619, 641, 643, 709, 727, 739, 797, 811, 823, 829, 853, 857, 877, 907, 983, 991, 1033, 1051, 1097, 1103, 1117, 1193, 1217, 1229, 1231, 1237

Offset: 1

Author

S. I. Dimitrov, Jul 07 2025

Keywords

• nonn
• easy

Examples

			(41, 61) is such a pair because sigma(41+1)=sigma(61+1) = 96.
		

Links

• S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Crossrefs

Cf. A000203, A000040, A008333, A385586 (a subsequence).

Programs

Mathematica

s={};Do[Do[If[DivisorSigma[1,Prime[m]+1]==DivisorSigma[1,Prime[n]+1],AppendTo[s,Prime[n]];Break[]],{m,n-1}],{n,203}];s (* James C. McMahon, Jul 08 2025 *)

PARI

isok(p) = my(s=sigma(p+1)); forprime(q=1, p-1, if (sigma(q+1)==s, return(q))); \\ Michel Marcus, Jul 07 2025