A391865 Numbers k such that A003415(k) == A276085(k) (mod 5^5), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 10, 15, 28, 2681, 3828, 5005, 5239, 10906, 12768, 13656, 13761, 16119, 16591, 22616, 26318, 26831, 33881, 37105, 39477, 40806, 42638, 54940, 55228, 62883, 63957, 64331, 70119, 76882, 79199, 84721, 86051, 91339, 92278, 105011, 112502, 115400, 124055, 125908, 129674, 131544, 135041, 140319, 145108, 145702, 152255

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..142

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
is_A391865(n) = !((A276085(n)-A003415(n))%(5^5));
(PARI) is_A391865(n) = { my(m=5^5, f = factor(n), pr=1, i=1, s = Mod(-A003415(n), m)); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= Mod(prime(i), m); i++); s += f[k, 2]*pr); (0==lift(s)); };

Crossrefs

Cf. A003415, A276085, A369650 (subsequence).

Cf. also A377878, A391864.

Sequence in context: A063610 A392601 A391864 * A369650 A392868 A181474

Adjacent sequences: A391862 A391863 A391864 * A391866 A391867 A391868

Keyword

nonn

Author

Antti Karttunen, Jan 16 2026

Status

approved