A065803 a(n) = (sigma_2(n) mod 2) * (sigma_2(n) mod 5). Residue-product modulo 2 and 5 of sum of square of divisors.

1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3

Offset

1,121

Comments

If n is square then sigma_2(n) is divisible by neither 2 nor 5. The product of residues is not always one. E.g., sigma_2(121) = 14673; mod 2 and mod 5 gives 1 and 3 residues. a(n)=3 for n=121, 361, 484, 841, 961 etc..

a(n)=4 for n=43681, 101761, 116281, 174724, 203401, 303601, 346921, ... - R. J. Mathar, Apr 02 2011

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Antti Karttunen, Table of n, a(n) for n = 1..101761 (terms 1..10000 from Charles R Greathouse IV)

Robert Price, Comments on A065803 concerning Elementary Cellular Automata, Jan 29 2016

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

a(n) = (A001157(n) mod 2) * (A001157(n) mod 5).

Maple

A001157 := proc(n) numtheory[sigma][2](n) ; end proc:
A065803 := proc(n) (A001157(n) mod 2)*(A001157(n) mod 5) ; end proc: # R. J. Mathar, Apr 02 2011

Mathematica

Array[Mod[#, 2] Mod[#, 5] &@ DivisorSigma[2, #] &, 121] (* Michael De Vlieger, Jan 19 2020 *)

Prog

(PARI) a(n)=if(issquare(n), sigma(n, 2)%5, 0) \\ Charles R Greathouse IV, Nov 19 2014

Crossrefs

Cf. A001157, A053866, A000290.

Sequence in context: A100267 A176935 A257228 * A160540 A186718 A319625

Adjacent sequences: A065800 A065801 A065802 * A065804 A065805 A065806

Keyword

easy,nonn

Author

Labos Elemer, Nov 21 2001

Extensions

Data section extended up to a(121) by Antti Karttunen, Jan 18 2020

Status

approved