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.

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

Author

Altug Alkan, Jan 30 2017

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Crossrefs

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

Programs

PARI

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

Extensions

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