A385478 - OEIS

A385478

a(n) is the smallest divisor of sigma(n) that is not element of the union of the sets of divisors of sigma(k) for 1 <= k < n; or 0 if no such divisor exists.

1, 3, 2, 7, 6, 12, 8, 5, 13, 9, 0, 14, 0, 24, 0, 31, 0, 39, 10, 21, 16, 36, 0, 30, 0, 0, 40, 56, 0, 72, 0, 63, 48, 27, 0, 91, 19, 0, 0, 45, 0, 96, 11, 84, 26, 0, 0, 62, 57, 93, 0, 49, 0, 120, 0, 0, 80, 0, 0, 168, 0, 0, 52, 127, 0, 144, 17, 126, 0, 0, 0, 65, 37

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OFFSET

1,2

COMMENTS

Conjecture: The divisors counted in A385467(n) are multiples of a(n).

LINKS

Felix Huber, Table of n, a(n) for n = 1..10000

EXAMPLE

The divisors of sigma(3) = 4 are {1, 2, 4}. Among these, 2 and 4 have not yet been counted in the sequence, so a(3) = 2.

The divisors of sigma(8) = 15 are {1, 3, 5, 15}. Among these, 5 and 15 have not yet been counted in the sequence, so a(8) = 5.

The divisors of sigma(11) = 12 are {1, 12}. Both divisors have already been counted in the sequence (1 in a(1) and 12 in a(6)), so a(11) = 0.

MAPLE

with(NumberTheory):

A385478:=proc(n)

option remember;

local d, s, t;

if n=1 then

[1, {1}]

else

d:=procname(n-1)[2];

s:=Divisors(sigma(n));

t:=s minus d;

if nops(t)>0 then

return [t[1], s union d]

else

return [0, d]

fi;

end proc;

seq(A385478(n)[1], n=1..73);

PROG

(PARI) a(n) = my(s=Set()); for(k=1, n-1, s=setunion(s, divisors(sigma(k)))); fordiv(sigma(n), d, if (!setsearch(s, d), return(d))); \\ Michel Marcus, Jul 02 2025

CROSSREFS

Cf. A000005, A000203, A027750, A062068, A385467, A385479.

Sequence in context: A122336 A122355 A175433 * A058646 A323635 A125718

Adjacent sequences: A385475 A385476 A385477 * A385479 A385480 A385481

KEYWORD

nonn,easy

AUTHOR

Felix Huber, Jul 01 2025

STATUS

approved