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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A116326 A031809

Adjacent sequences:  A324708 A324709 A324710 * A324712 A324713 A324714

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Mar 13 2019

STATUS

approved

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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)