A324711 Number x such that sigma(x) = Sum_{i=1..k} {sigma(x/p_i)}, where p_i are the k prime factors of x.

8580, 16632, 24840, 35910, 38280, 53130, 161040, 186732, 276276, 429780, 598290, 833112, 1232616, 1297890, 1631448, 2661330, 2781000, 2875740, 3111108, 3233790, 3449640, 3504816, 3754920, 4901160, 5185488, 5211570, 5948250, 6749028, 8066640, 9006984, 10750080

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Example

Prime factors of 8580 are 2, 3, 5, 11, 13 and sigma(8580) = 28224, sigma(8580/2) + sigma(8580/3) + sigma(8580/5) + sigma(8580/11) + sigma(8580/13) = 12096 + 7056 + 4704 + 2352 + 2016 = 28224.

Maple

with(numtheory): P:=proc(q) local k, n; for n from 1 to q do
if sigma(n)=add(sigma(n/k), k=factorset(n)) then print(n);
fi; od; end: P(10^9);

Mathematica

Select[Range[2, 60000], DivisorSigma[1, #] == Total@DivisorSigma[1, #/FactorInteger[#][[;; , 1]]] &] (* Amiram Eldar, Mar 20 2019 *)

Prog

(PARI) isok(x) = my(f=factor(x)[, 1]~); sigma(x) == sum(k=1, #f, sigma(x/f[k])); \\ Michel Marcus, Mar 15 2019

Crossrefs

Cf. A000203, A324710.

Sequence in context: A243839 A287119 A156846 * A221053 A370972 A370970

Adjacent sequences: A324708 A324709 A324710 * A324712 A324713 A324714

Keyword

nonn

Author

Paolo P. Lava, Mar 13 2019

Status

approved