A281687 -id:A281687 - cp's OEIS frontend

A282778 First differences of A281687.

0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, -1, 1, 0, 2, -1, 1, -1, 1, 0, 2, -1, 2, -2, 1, -1, 2, -1, 2, -3, 1, 1, 1, -1, 3, -2, -1, 1, 0, -1, 3, -1, 0, 0, 2, -1, 4, -3, 0, 0, 1, -2, 4, -4, 3, -2, 3, -3, 4, -2, 1, -1, 2, -3, 5, -3, 2, -3, 3, -2, 3, -2, 0, 1

Offset: 1

Altug Alkan, Feb 21 2017

sign

Numbers n such that a(n) = 0 are 1, 2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 17, 18, 22, 28, 47, 51, 52, 57, 58, 81, 111, 112, 195, 201 according to the b-file. Can there be other values of n such that a(n) = 0? See also graph of this sequence.

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Alternative Scatterplot of A282778

Cf. A281687.

a281687(n) = sum(k=1, n, istotient(k) && istotient(2*n-k));
a(n) = a281687(n+1) - a281687(n);

a(n) = A281687(n+1) - A281687(n).

A280867 Least k such that k is the sum of two totient numbers (A002202) in exactly n ways, or 0 if no such k exists.

Original entry on oeis.org

2, 8, 12, 20, 24, 32, 40, 50, 48, 62, 60, 64, 76, 102, 88, 108, 120, 128, 112, 136, 152, 148, 186, 168, 180, 192, 184, 216, 252, 236, 208, 220, 244, 232, 308, 268, 280, 292, 336, 304, 368, 328, 384, 364, 352, 408, 440, 376, 432, 400, 436, 388, 448, 492, 460, 484, 472, 548

Offset: 1

Altug Alkan, Jan 28 2017

nonn

Least k such that A281687(k/2) = n, or 0 if no such k exists.

See also graph of A001172 for similar points.

			a(4) = 20 because 20 = 2 + 18 = 4 + 16 = 8 + 12 = 10 + 10; 2, 4, 8, 10, 12, 16, 18 are in A002202 and 20 is the least number with this property.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000010, A001172, A002202, A281687.

a281687(n) = sum(k=1, n, istotient(k) && istotient(2*n-k));
a(n) = my(k=1); while(a281687(k) != n, k++); 2*k;

do(n)=my(u=select(istotient, [1..n]),v=vector(n),t); for(i=1,#u, for(j=i,#u, t=u[i]+u[j]; if(t>n, break); v[t]++)); t=vector(vecmax(v)); for(i=1,#v, if(v[i] && t[v[i]]==0, t[v[i]]=i)); for(i=1,#t, if(t[i]==0, return(t[1..i-1]))); t \\ Charles R Greathouse IV, Jan 29 2017

A281816 Least k such that phi(k) is the sum of two totient numbers (A002202) in exactly n ways, or 0 if no such k exists.

Original entry on oeis.org

1, 3, 11, 13, 23, 29, 37, 41, 81, 53, 67, 61, 73, 97, 103, 89, 109, 143, 139, 113, 137, 157, 149

Offset: 0

Altug Alkan, Jan 30 2017

For the first 10000 terms of A281687, only A281687(93) = 23 and 2 * 93 = 186 is not a totient number. With this observation if we consider the scatterplot of A281687, a(23) is probably equal to 0, but this is still unproved at this moment. So this sequence has keyword "more".

a(24) - a(71) are 173, 181, 193, 235, 247, 301, 271, 229, 253, 289, 233, 519, 269, 281, 293, 337, 317, 439, 349, 397, 373, 353, 409, 575, 535, 433, 401, 571, 389, 449, 551, 461, 879, 623, 577, 743, 521, 509, 557, 685, 689, 569, 661, 593, 767, 709, 653, 641.

			a(3) = 13 because phi(13) = 12 = 2 + 10 = 4 + 8 = 6 + 6; 2, 4, 6, 8, 10 are in A002202 and 13 is the least number with this property.

Cf. A000010, A002202, A280867, A281687, A281875.

c(n) = sum(k=1, n\2, istotient(k) && istotient(n-k));
a(n) = my(k=1); while(c(eulerphi(k)) != n, k++); k;

a(0) = 1 prepended by Chai Wah Wu, Feb 03 2017

cp's OEIS Frontend

A282778 First differences of A281687.

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A280867 Least k such that k is the sum of two totient numbers (A002202) in exactly n ways, or 0 if no such k exists.

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A281816 Least k such that phi(k) is the sum of two totient numbers (A002202) in exactly n ways, or 0 if no such k exists.

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