A368921 -id:A368921 - cp's OEIS frontend

A368922 a(n) = n' - n''*2, where n' is the arithmetic derivative of n, A003415(n) and n'' is the second arithmetic derivative, A068346(n).

0, 0, 1, 1, -4, 1, 3, 1, -20, -4, 5, 1, -48, 1, -3, -16, -128, 1, 1, 1, -64, -4, 11, 1, -52, -4, -1, -27, -128, 1, 29, 1, -272, -4, 17, -20, -124, 1, 1, -48, -76, 1, 39, 1, -176, 7, 5, 1, -368, -4, -33, -28, -128, 1, -135, -48, -100, -4, 29, 1, -100, 1, 5, 11, -1088, -24, 59, 1, -240, -4, 57, 1, -284, 1, 7, 23, -272

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, A334261 (positions of -4's), A368701, A368921.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A368922(n) = { my(u=A003415(n)); (u-2*A003415(u)); };

a(n) = A003415(n) - 2*A068346(n).

a(n) = A368921(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

A368922 a(n) = n' - n''*2, where n' is the arithmetic derivative of n, A003415(n) and n'' is the second arithmetic derivative, A068346(n).

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