A119240 -id:A119240 - cp's OEIS frontend

A334117 Odd numbers with abundancy >= 3/2; that is, numbers m such that sigma(m) >= 3m/2.

15, 21, 45, 63, 75, 99, 105, 117, 135, 147, 153, 165, 171, 189, 195, 207, 225, 231, 255, 273, 285, 297, 315, 345, 351, 357, 375, 399, 405, 429, 435, 441, 459, 465, 483, 495, 513, 525, 555, 561, 567, 585, 609, 615, 621, 627, 645, 651, 663, 675, 693, 705, 735, 741, 759

Offset: 1

Charles R Greathouse IV, Apr 14 2020

nonn

The density of this sequence exists and is positive. If m is in this sequence, then so is mk, where k is a positive odd number (see A334118).

The numbers of terms that do not exceed 10^k, for k = 2, 3, ..., are 6, 73, 700, 7179, 70759, 709928, 7101533, 70999783, 709865878, 7098956986, ... . Apparently, the asymptotic density of this sequence equals 0.0709... . - Amiram Eldar, Dec 28 2024

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A334118, A000203, A005231, A119240.

Select[Range[1, 1000, 2], DivisorSigma[-1, #] >= 3/2 &] (* Amiram Eldar, Dec 28 2024 *)

PARI
```
is(n)=n%2 && sigma(n,-1)>=3/2
```

forfactored(n=1,10^4, if(sigma(n,-1)>=3/2 && n[1]%2, print1(n[1]", ")))

A334118 Primitive terms of A334117: odd numbers m such that sigma(m, -1) >= 3/2 with no proper divisors sharing this property.

Original entry on oeis.org

15, 21, 99, 117, 153, 171, 207, 429, 561, 627, 663, 741, 759, 783, 837, 957, 999, 1023, 1107, 1161, 1269, 1431, 1593, 1647, 1809, 1917, 1925, 1971, 2133, 2275, 2695, 2975, 3185, 4235, 5005, 6545, 6723, 7209, 7315, 7735, 7857, 8091, 8181, 8343, 8645, 8667, 8829, 8855

Offset: 1

Charles R Greathouse IV, Apr 14 2020

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A334117, A000203, A005231, A119240.

Select[Range[1, 10^4, 2], DivisorSigma[-1, #] >= 3/2 && Max[DivisorSigma[-1, Most[Divisors[#]]]] < 3/2 &] (* Amiram Eldar, Dec 28 2024 *)

list(lim)=my(v=List(), k); forfactored(n=15,lim\1, if(sigma(n,-1)>=3/2 && (k=n[1])%2, for(i=1,#v, if(k%v[i]==0, next(2))); listput(v,k))); Vec(v)

cp's OEIS Frontend

A334117 Odd numbers with abundancy >= 3/2; that is, numbers m such that sigma(m) >= 3m/2.

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A334118 Primitive terms of A334117: odd numbers m such that sigma(m, -1) >= 3/2 with no proper divisors sharing this property.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI