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

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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..53.

Example

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.

Mathematica

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

Prog

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

Crossrefs

A323726 is a subsequence.

Apart from the first term, a subsequence of A334117.

Cf. A000203, A053222, A231546, A333038, A333039, A333040.

Sequence in context: A144422 A327053 A135444 * A323726 A087886 A123754

Adjacent sequences: A333038 A333039 A333040 * A333042 A333043 A333044

Keyword

nonn

Author

Bernard Schott, Apr 14 2020

Status

approved