A325652 a(n) = the sum of numbers k such that sigma(k) = sigma(n).

1, 2, 3, 4, 5, 17, 7, 8, 9, 27, 17, 12, 13, 52, 52, 41, 27, 18, 19, 87, 52, 22, 52, 121, 41, 87, 27, 67, 29, 253, 52, 32, 115, 87, 115, 36, 37, 121, 67, 187, 87, 250, 43, 192, 45, 253, 115, 123, 49, 50, 253, 149, 87, 292, 253, 292, 136, 187, 121, 663, 61, 250

Offset

1,2

Comments

a(n)=n if n is in A211656, otherwise a(n) > n. - Robert Israel, Jul 04 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(6) = 17 because sigma(6) = sigma(11) = 12; 6 + 11 = 17.

Maple

N:= 1000: # to get a(n) before the first n with sigma(n) > N
S:= map(numtheory:-sigma, [$1..N-1]):
m:=min(select(t -> S[t]>N, [$1..N-1]))-1:
1, seq(convert(select(s -> S[s]=S[n], [$1..S[n]-1]), `+`), n=2..m); # Robert Israel, Jul 04 2019

Mathematica

a[n_] := Block[{s = DivisorSigma[1, n]}, Sum[Boole[s == DivisorSigma[1, k]] k, {k, s}]]; Array[a, 62] (* Giovanni Resta, Jul 03 2019 *)

Prog

(Magma) [&+[k: k in[1..10000] | SumOfDivisors(k) eq SumOfDivisors(n)]: n in [1..100]]
(PARI) a(n) = {my(s=sigma(n)); sum(k=1, s, (sigma(k)==s)*k); } \\ Michel Marcus, May 12 2019

Crossrefs

Cf. A000203, A211656, A275987, A325651.

See A070242 and A325653 for number and product of such numbers k.

Sequence in context: A240906 A117885 A030574 * A283653 A162657 A333046

Adjacent sequences: A325649 A325650 A325651 * A325653 A325654 A325655

Keyword

nonn,look

Author

Jaroslav Krizek, May 12 2019

Status

approved