A373071 Integers k such that k-1 is a multiple of Sum_{prime|k}(prime-1).

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 65, 66, 67, 71, 73, 79, 81, 83, 89, 91, 97, 101, 103, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 149, 151, 154, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199

Offset: 1

Author

Rafik Khalfi, May 25 2024

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Robert C. Vaughan and Kevin L. Weis, On sigma-phi numbers, Mathematika 48 (2001), 169-189.

Crossrefs

Cf. A055631.

A246655 is a subsequence.

Programs

Maple

f:= proc(n)
 add( d-1, d= numtheory[factorset](n));
 end proc:
results := []:
for n from 2 to 1000 do  # Adjust the range as needed
 if mod(n-1, f(n)) = 0 then
 results := [op(results), n];
 end if;
end do;
results;

Mathematica

Select[Range[2, 200], Divisible[# - 1, Total[FactorInteger[#][[;; , 1]] - 1]] &] (* Amiram Eldar, May 26 2024 *)

PARI

isok(k) = (k>1) && (((k-1) % vecsum(apply(x->(x-1), factor(k)[,1]))) == 0); \\ Michel Marcus, May 26 2024