A054010 -id:A054010 - cp's OEIS frontend

A055719 d(n)-1 | n and n is not prime.

4, 6, 15, 16, 20, 21, 27, 33, 39, 42, 45, 50, 51, 56, 57, 69, 70, 75, 87, 93, 105, 111, 120, 123, 129, 132, 141, 154, 159, 162, 175, 177, 182, 183, 189, 198, 201, 210, 213, 219, 220, 231, 237, 238, 245, 249, 256, 266, 267, 270, 273, 275, 291, 303, 308, 309, 321

Offset: 1

Robert G. Wilson v, Jun 09 2000

nonn

Composite integers divisible by 1 less than the number of their divisors.

This is, composite members of A054010. - Carl R. White, Jul 11 2012

Carl R. White, Table of n, a(n) for n = 1..10000

Cf. A054010.

Do[ If[ !PrimeQ[ n ], If[ IntegerQ[ n/(DivisorSigma[ 0, n ]-1) ], Print[ n ] ] ], {n, 1, 500} ]
Select[Range[2,400],!PrimeQ[#]&&Divisible[#,DivisorSigma[0,#]-1]&] (* Harvey P. Dale, Mar 13 2013 *)

A279455 Numbers n such that the number of nonprime divisors of n divides n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 34, 37, 38, 41, 43, 44, 46, 47, 48, 52, 53, 54, 58, 59, 61, 62, 67, 68, 70, 71, 73, 74, 76, 79, 80, 82, 83, 86, 89, 90, 92, 94, 97, 101, 103, 105, 106, 107, 109, 110, 112, 113, 116, 118

Offset: 1

Ilya Gutkovskiy, Dec 12 2016

Numbers n such that A033273(n) divides n.
Fixed points of lcm(n, tau(n)-omega(n)), where tau(n) is the number of divisors of n (A000005) and omega(n) is the number of distinct primes dividing n (A001221).
All primes (A000040) are included in the sequence.
All even semiprimes (A100484) are included in the sequence.

			12 is in the sequence because 12 has 6 divisors {1,2,3,4,6,12} out of which 4 are nonprimes {1,4,6,12} and 4 divides 12.

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000005, A000040, A001221, A033950, A033273, A054010, A075592.

Select[Range[150], Divisible[#1, DivisorSigma[0, #1] - PrimeNu[#1]] & ]

isok(n) = denominator(n/sumdiv(n, d, !isprime(d))) == 1; \\ Michel Marcus, Dec 17 2016

A306307 Numbers that are divisible by the number of their nontrivial divisors.

Original entry on oeis.org

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

Offset: 1

Todor Szimeonov, Feb 05 2019

nonn

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.

			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.

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

Cf. A070824, A054010, A033950.

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

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

More terms from Michel Marcus, Feb 17 2019

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A055719 d(n)-1 | n and n is not prime.

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A279455 Numbers n such that the number of nonprime divisors of n divides n.

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A306307 Numbers that are divisible by the number of their nontrivial divisors.

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