A385467 - OEIS

A385467

a(n) is the number of divisors of sigma(n) that have not yet been counted in the sequence.

1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0, 1, 0, 1, 0, 1, 2, 2, 2, 1, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 2, 0, 0, 2, 0, 1, 3, 1, 2, 0, 0, 2, 1, 1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 3, 1, 0, 0, 0, 2, 2, 1, 0, 3, 0, 0, 0, 1, 1, 0, 0, 2, 1, 3, 0, 1

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OFFSET

1,3

LINKS

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

FORMULA

a(n) = |divisors(sigma(n)) minus Union_{k=1..n-1} divisors(sigma(k))|.

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) = 2.

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):

A385467:=proc(n)

option remember;

local d, s;

if n=1 then

[1, {1}]

else

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

s:=Divisors(sigma(n));

return [nops(s minus d), s union d]

fi;

end proc;

seq(A385467(n)[1], n=1..88);

PROG

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

CROSSREFS

Partial sums give A385479.

Cf. A000005, A000203, A027750, A062068, A385478.

Sequence in context: A309228 A309778 A143223 * A063993 A353445 A115722

Adjacent sequences: A385464 A385465 A385466 * A385468 A385469 A385470

KEYWORD

nonn,easy

AUTHOR

Felix Huber, Jul 01 2025

STATUS

approved