The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A333041

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A333041

Odd numbers m such that sigma(m) > sigma(m-1).
(history; published version)

#11 by Charles R Greathouse IV at Tue Apr 14 16:01:06 EDT 2020

STATUS

editing

approved

#10 by Charles R Greathouse IV at Tue Apr 14 15:52:36 EDT 2020

PROG

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

#9 by Charles R Greathouse IV at Tue Apr 14 15:51:33 EDT 2020

CROSSREFS

A323726 is a subsequence.

Apart from the first term, a subsequence of A334117.

Cf. A323726 (subsequence)

STATUS

proposed

editing

#8 by Amiram Eldar at Tue Apr 14 14:13:30 EDT 2020

STATUS

editing

proposed

#7 by Amiram Eldar at Tue Apr 14 14:13:20 EDT 2020

MATHEMATICA

Select[2 * Range[1001000] + 1, DivisorSigma[1, #] > DivisorSigma[1, # - 1] &] (* Amiram Eldar, Apr 14 2020 *)

#6 by Amiram Eldar at Tue Apr 14 14:13:07 EDT 2020

MATHEMATICA

Select[2 * Range[100] + 1, DivisorSigma[1, #] > DivisorSigma[1, # - 1] &] (* Amiram Eldar, Apr 14 2020 *)

STATUS

proposed

editing

#5 by Bernard Schott at Tue Apr 14 13:36:29 EDT 2020

STATUS

editing

proposed

#4 by Bernard Schott at Tue Apr 14 13:36:11 EDT 2020

EXAMPLE

sigma(63) = 1+3+7+9+21+63 = 104 > sigma(62) = 1+2+31+62=96 and 63 is in the sequence.

#3 by Bernard Schott at Tue Apr 14 13:33:54 EDT 2020

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.

CROSSREFS

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

Cf. A323726 (subsequence)

#2 by Bernard Schott at Tue Apr 14 13:30:23 EDT 2020

NAME

allocated for Bernard SchottOdd numbers m such that sigma(m) > sigma(m-1).

DATA

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.

KEYWORD

allocated

nonn

AUTHOR

Bernard Schott, Apr 14 2020

STATUS

approved

editing