A066341 Sum of distinct terms in n-th row of Fermat's triangle.

1, 1, 1, 1, 8, 1, 1, 1, 12, 1, 14, 1, 16, 17, 1, 1, 20, 1, 22, 23, 24, 1, 26, 1, 28, 1, 30, 1, 94, 1, 1, 35, 36, 37, 38, 1, 40, 41, 42, 1, 130, 1, 46, 47, 48, 1, 50, 1, 52, 53, 54, 1, 56, 57, 58, 59, 60, 1, 184, 1, 64, 65, 1, 67, 202, 1, 70, 71, 214, 1, 74, 1, 76, 77, 78, 79, 238, 1

Offset

2,5

Links

Antti Karttunen, Table of n, a(n) for n = 2..13737 (terms 2..2000 from Muniru A Asiru)

Example

Fermat's triangle (A066340) is {1}, {1, 1}, {1, 0, 1}, {1, 1, 1, 1}, {1, 4, 3, 4, 1}, ... and the distinct terms in each row are {1}, {1}, {0, 1}, {1}, {1, 3, 4}, ... with sums 1, 1, 1, 1, 8, ...

Mathematica

Plus@@@(Union/@Table[ (PowerMod[ #, EulerPhi[ k ], k ])&/@ Range[ k-1 ], {k, 2, 256} ]) or equivalently Table[ w=Length[ FactorInteger[ k ]]; (2^(w-1)-1)*k+2^(w-1), {k, 2, 256} ]

Prog

(PARI) A066341(n) = { my(ph = eulerphi(n), m=Map(), t, s=0); for(k=1, n-1, t = ((k^ph)%n); if(!mapisdefined(m, t), s += t; mapput(m, t, t))); (s); }; \\ Antti Karttunen, Aug 06 2018
(GAP) List(List(List([2..80], n->List([1..n-1], m->PowerMod(m, Phi(n), n))), Set), Sum); # Muniru A Asiru, Aug 06 2018

Crossrefs

Cf. A066340.

Sequence in context: A316786 A011264 A276405 * A181064 A010153 A360970

Adjacent sequences: A066338 A066339 A066340 * A066342 A066343 A066344

Keyword

easy,nonn

Author

Wouter Meeussen, Jan 01 2002

Status

approved