A354928 Numbers k such that A047994(k) = A344005(k).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 22, 23, 25, 26, 27, 29, 31, 32, 34, 37, 38, 41, 43, 46, 47, 49, 50, 53, 54, 58, 59, 61, 62, 64, 67, 71, 73, 74, 79, 81, 82, 83, 86, 89, 94, 97, 98, 101, 103, 106, 107, 109, 113, 118, 121, 122, 125, 127, 128, 131, 134, 137, 139, 142, 146, 149, 151, 157, 158

Offset: 1

Author

Antti Karttunen, Jun 13 2022

Keywords

• nonn

Crossrefs

Cf. A346608 (complement), A354924 (characteristic function).

Cf. A047994, A344005.

Positions of zeros in A346607.

Programs

Mathematica

f[p_, e_] := p^e - 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; uphi[1] = 1; q[n_] := Module[{m = 1, u = uphi[n]}, While[m <= u && ! Divisible[m*(m + 1), n], m++]; m == u]; Select[Range[160], q] (* Amiram Eldar, Jun 13 2022 *)

PARI

A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354924(n) = (A047994(n)==A344005(n));
isA354928(n) = A354924(n);