A368922 -id:A368922 - cp's OEIS frontend

A368921 a(n) = n' - n'', where n' is the arithmetic derivative of n, A003415(n) and n'' is its second arithmetic derivative, A068346(n).

0, 0, 1, 1, 0, 1, 4, 1, -4, 1, 6, 1, -16, 1, 3, -4, -48, 1, 11, 1, -20, 3, 12, 1, -4, 3, 7, 0, -48, 1, 30, 1, -96, 5, 18, -4, -32, 1, 11, -16, -4, 1, 40, 1, -64, 23, 15, 1, -128, 5, 6, -4, -36, 1, -27, -16, -4, 9, 30, 1, -4, 1, 19, 31, -448, -3, 60, 1, -84, 11, 58, 1, -64, 1, 23, 39, -96, -3, 70, 1, -192, -108, 42

Offset: 0

Antti Karttunen, Jan 10 2024

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Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A003415, A068346, A348329 (positions of 0's), A368922.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A368921(n) = { my(u=A003415(n)); (u-A003415(u)); };

a(n) = A003415(n) - A068346(n).

a(n) = A368922(n) + A068346(n).

A369052 a(n) = n - n'*2, where n' is the arithmetic derivative of n, A003415.

Original entry on oeis.org

0, 1, 0, 1, -4, 3, -4, 5, -16, -3, -4, 9, -20, 11, -4, -1, -48, 15, -24, 17, -28, 1, -4, 21, -64, 5, -4, -27, -36, 27, -32, 29, -128, 5, -4, 11, -84, 35, -4, 7, -96, 39, -40, 41, -52, -33, -4, 45, -176, 21, -40, 11, -60, 51, -108, 23, -128, 13, -4, 57, -124, 59, -4, -39, -320, 29, -56, 65, -76, 17, -48, 69, -240, 71

Offset: 0

Antti Karttunen, Jan 17 2024

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Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A003415.

Cf. also A068719, A168036, A368921, A368922.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369052(n) = (n-2*A003415(n));

a(n) = n - 2*A003415(n).

a(n) = -(A003415(n)+A168036(n)).

cp's OEIS Frontend

A368921 a(n) = n' - n'', where n' is the arithmetic derivative of n, A003415(n) and n'' is its second arithmetic derivative, A068346(n).

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