A345005 Odd numbers whose arithmetic derivative (A003415) is equal to Dedekind psi (A001615) applied to the same number.

81, 3375, 15625, 231525, 713097, 1058841, 1500625, 4348377, 5764801, 16891497, 163555875, 209548647, 239010993, 239160735, 254205875, 267651475, 405189675, 451699875, 958403475, 1050284375, 1213014231, 1501534375, 1695809375, 1809323971, 1942143291

Offset: 1

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn
• more

Comments

Conjectured to be also the odd numbers k for which A344998(k) = A344999(k).

Crossrefs

Odd terms in A301939, but see also A345003.

Cf. A001615, A003415, A344998, A344999.

Programs

PARI

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA345005(n) = ((n%2)&&(A003415(n)==A001615(n)));