

A306307


Numbers that are divisible by the number of their nontrivial divisors.


0



4, 6, 8, 9, 10, 12, 14, 20, 22, 24, 25, 26, 28, 30, 32, 34, 38, 42, 44, 46, 48, 49, 52, 54, 58, 60, 62, 66, 68, 74, 76, 78, 80, 81, 82, 86, 90, 92, 94, 102, 106, 112, 114, 116, 118, 121, 122, 124, 134, 138, 140, 142, 146, 148, 150, 158, 160, 164, 166, 168, 169, 172, 174
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OFFSET

1,1


COMMENTS

We may define the number of divisors of a number n in four ways:
(1) A070824(n) = number of nontrivial or real divisors: 1 < d < n;
(2) variant of A032741(n) = number of small divisors: 1 and real divisors;
(3) A032741(n) = number of big or proper divisors: real divisors and n;
(4) A000005(n) = number of all divisors of n: 1, n and real divisors.
The case (1), divisibility through the number of nontrivial divisors, defines this sequence.


REFERENCES

T. Szimeonov, A szĂˇmok [The numbers], Budapest, 2019, VVMA, 124 p.


LINKS

Table of n, a(n) for n=1..63.


EXAMPLE

1 and the prime numbers do not have any nontrivial divisors; A070824(n) is 0 for n=1 or a prime, and so they are not terms.
The only nontrivial divisor of 4 is 2, so A070824(4) = 1; 4 is divisible by 1, so 4 is a term.
A070824(15) = 2, and 15 is not divisible by 2, so 15 is not a term.


MATHEMATICA

seqQ[n_] := (nd = DivisorSigma[0, n]  2) > 0 && Divisible[n, nd]; Select[Range[200], seqQ] (* Amiram Eldar, Mar 11 2019 *)


PROG

(PARI) f(n) = if (n==1, 0, numdiv(n)2); \\ A070824
isok(n) = f(n) && !frac(n/f(n)); \\ Michel Marcus, Feb 17 2019


CROSSREFS

Cf. A070824, A054010, A033950.
Sequence in context: A128510 A109289 A066071 * A248010 A067013 A141607
Adjacent sequences: A306304 A306305 A306306 * A306308 A306309 A306310


KEYWORD

nonn


AUTHOR

Todor Szimeonov, Feb 05 2019


EXTENSIONS

More terms from Michel Marcus, Feb 17 2019


STATUS

approved



