A007964 Numbers k such that product of proper divisors of k is <= k; i.e., product of divisors of k is <= k^2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106

Offset: 1

Author

R. Muller

Keywords

• nonn
• easy

Comments

Numbers which are the product of up to two primes (not necessarily distinct) or the cube of a prime. Alternatively, numbers having prime decomposition p*q, where q either is distinct from p or equals p^k for 0 <= k <= 2.

Corresponds to numbers having at most four divisors. (For numbers with exactly four divisors see A030513.) - Lekraj Beedassy, Sep 23 2003

For n > 3: numbers that can occur as fourth divisors; union of A000040, A001248, A006881 and A030078. - Reinhard Zumkeller, May 15 2006

References

• Liu Hongyan and Zhang Wenpeng, On the simple numbers and the mean value properties, Smarandache Notions (Book Series, Vol. 14), American Research Press, 2004; pp. 171-175.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• F. Smarandache, Only Problems, Not Solutions! (listing the sequence as the "simple numbers" in Unsolved Problem: 23 p.23).

Crossrefs

Cf. A007955, A058080.

Programs

Mathematica

Select[Range[100], DivisorSigma[0, #] < 5 &] (* Amiram Eldar, Apr 30 2020 *)

PARI

is(n)=numdiv(n)<5 \\ Charles R Greathouse IV, Sep 16 2015

Extensions

Description corrected by Henry Bottomley, Nov 24 2000