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, 2215505331

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..26.

Prog

(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));

Crossrefs

Odd terms in A301939, but see also A345003.

Cf. A001615, A003415, A344998, A344999.

Sequence in context: A254415 A017744 A232945 * A223477 A237842 A223501

Adjacent sequences: A345002 A345003 A345004 * A345006 A345007 A345008

Keyword

nonn

Author

Antti Karttunen, Jun 05 2021

Extensions

a(26) from Jinyuan Wang, Sep 06 2025

Status

approved