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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

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

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).

EXAMPLE

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

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

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: A014999 A227291 A271102 * A326072 A304362 A330682

Adjacent sequences:  A065800 A065801 A065802 * A065804 A065805 A065806

KEYWORD

easy,nonn

AUTHOR

Labos Elemer, Nov 21 2001

STATUS

approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)