A325651 -id:A325651 - cp's OEIS frontend

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

Jaroslav Krizek, May 12 2019

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

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

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

Cf. A000203, A211656, A275987, A325651.

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

[&+[k: k in[1..10000] | SumOfDivisors(k) eq SumOfDivisors(n)]: n in [1..100]];

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

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

a(n) = {my(s=sigma(n)); sum(k=1, s, (sigma(k)==s)*k);} \\ Michel Marcus, May 12 2019

A325653 a(n) = the product of numbers k such that sigma(k) = sigma(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 66, 7, 8, 9, 170, 66, 12, 13, 4830, 4830, 400, 170, 18, 19, 21320, 651, 22, 4830, 53808, 400, 21320, 27, 1092, 29, 274833900, 651, 32, 54285, 1802, 54285, 36, 37, 53808, 1092, 206480, 21320, 13835052, 43, 237380, 45, 274833900, 54285, 3600, 49

Offset: 1

Jaroslav Krizek, May 12 2019

nonn

			a(6) = 66 because sigma(6) = sigma(11) = 12; 6 * 11 = 66.

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

Cf. A000203, A275987, A325651.

See A070242 and A325652 for number and sum of such numbers k.

[&*[k: k in[1..10000] | SumOfDivisors(k) eq SumOfDivisors(n)]: n in [1..100]];

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:
seq(convert(select(s -> S[s]=S[n], [$1..S[n]-1]),`*`), n=1..m); # Robert Israel, Jul 04 2019

a[n_] := Block[{s = DivisorSigma[1, n]}, Product[Which[s == DivisorSigma[1, k], k, True, 1], {k, s}]]; Array[a, 49] (* Giovanni Resta, Jul 03 2019 *)

a(n) = {my(s=sigma(n)); prod(k=1, s, if ((sigma(k)==s), k, 1));} \\ Michel Marcus, May 12 2019

cp's OEIS Frontend

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

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