A334117 -id:A334117 - cp's OEIS frontend

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

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)

A333041 Odd numbers m such that sigma(m) > sigma(m-1).

Original entry on oeis.org

3, 63, 75, 135, 147, 195, 255, 315, 399, 405, 459, 483, 495, 525, 555, 567, 615, 627, 663, 675, 693, 735, 759, 765, 795, 819, 855, 915, 945, 975, 999, 1035, 1095, 1125, 1155, 1215, 1239, 1287, 1323, 1395, 1455, 1515, 1539, 1575, 1647, 1659, 1683, 1755, 1785, 1815, 1827, 1845, 1875

Offset: 1

Bernard Schott, Apr 14 2020

nonn

The odd terms of A333038 [sigma(m) <= sigma(m-1)] represent about 95% of the data, so the odd integers that do not satisfy this relation are proposed here.
Except for 3, there are no prime powers in this sequence.
It appears that most of the terms are divisible by 3; the two smallest exceptions are 13475 and 17255 (see A323726).
Odd (and even) numbers such that sigma(m) = sigma(m-1) are in A231546.

			sigma(63) = 1+3+7+9+21+63 = 104 > sigma(62) = 1+2+31+62=96 and 63 is in the sequence.
sigma(77) = 1+7+11+77 = 96 < sigma(76) = 1+2+4+19+38+76 = 140 and 77 is not a term.

A323726 is a subsequence.
Apart from the first term, a subsequence of A334117.
Cf. A000203, A053222, A231546, A333038, A333039, A333040.

Select[2 * Range[1000] + 1, DivisorSigma[1, #] > DivisorSigma[1, # - 1] &] (* Amiram Eldar, Apr 14 2020 *)

is(n)=n%2 && sigma(n)>sigma(n-1) \\ Charles R Greathouse IV, Apr 14 2020

cp's OEIS Frontend

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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