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

Author

Labos Elemer, Nov 21 2001

Keywords

• easy
• nonn

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

Crossrefs

Cf. A001157, A053866, A000290.

Programs

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 *)

PARI

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

Formula

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

Extensions

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