1,1

Sequence is generated by A007850(n). For example: 30, 858, 1722 (30 = 2*3*5, 858 = 2*3*11*13, 1722 = 2*3*11*13) generate numbers of the form 2^a*3^b*5^c (A143207), 2^a*3^b*7^c*41^d, 2^a*3^b*11^c*13^d, (a,b,c,d => 1), which are in the sequence.

Equivalently, numbers k such that Sum_{p|k} 1/p - Product_{p|k} 1/p, where p are the prime divisors of k, is a positive integer. All these terms have at least 3 prime factors. When k is a term and p is a prime divisor of k, then p*k is another term (see Diophante link). - Bernard Schott, Dec 19 2021

Amiram Eldar, Table of n, a(n) for n = 1..4233 (terms below 10^10)

Diophante, A1862 - Inversons les facteurs (in French).

For k = 30 = 2*3*5, 1/(Sum_{p|n} (1/p) - 1) = 1/(1/2 + 1/3 + 1/5 - 1) = 30 hence 30 is in the sequence.

Select[Range[4320], (sum = Plus @@ (1/FactorInteger[#][[;; , 1]])) > 1 && IntegerQ[1/(sum - 1)] &] (* Amiram Eldar, Feb 03 2020 *)

(Python)

from sympy import factorint

from fractions import Fraction

def ok(n):

s = sum(Fraction(1, p) for p in factorint(n))

return s > 1 and (s - 1).numerator == 1

print([k for k in range(1, 4501) if ok(k)]) # Michael S. Branicky, Dec 19 2021

(PARI) isok(k) = my(f=factor(k), x=1/(sum(i=1, #f~, 1/f[i, 1]) -1)); (x>1) && (denominator(x)==1); \\ Michel Marcus, Dec 19 2021

Cf. A007850.

A143207 is a subsequence.

Sequence in context: A249674 A050519 A358756 * A143207 A359410 A108454

Adjacent sequences: A069816 A069817 A069818 * A069820 A069821 A069822

easy,nonn

Benoit Cloitre, Apr 28 2002

approved