A388269 - OEIS

A388269

Odd numbers k for which A000005(k) >= A017665(k), where A000005 is the number of divisors function, and A017665 is the numerator of the abundancy ratio, sigma(k)/k.

1, 544635, 931095, 6517665, 14705145, 15828615, 22330035, 45623655, 49348035, 110800305, 161756595, 173369889, 249987465, 345436245, 593107515, 775602135, 779372685, 866849445, 1573450515, 1598690115, 1870569855, 2253808557, 2749862115, 2947288113, 7108165449, 10082827755, 11190830805, 11269042785, 14827687875

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OFFSET

1,2

COMMENTS

Odd numbers k such that A388270(k) >= A000203(k).

All odd terms of A001599 and of A007691 are also included in this sequence. It has been conjectured that both contain only one odd term, their initial 1.

Only five of the 52 initial terms are also in A228058: 866849445, 2253808557, 2947288113, 7108165449, 26900273673, while 1 and 173369889 are the only squares among the 52 initial terms.

Question: After the initial 1, is this a subsequence of A388277? - Antti Karttunen, Dec 16 2025

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..52 (all terms < 10^12)

David A. Corneth, First 52 terms from bfile and 41 other terms < 10^14 (might miss terms < 10^14).

Index entries for sequences where odd perfect numbers must occur, if they exist at all.

FORMULA

{k | k == 1 (mod 2), A000203(k) <= A000005(k)*A009194(k)}.

EXAMPLE

k = 173369889 = (3*3*7*11*19)^2 is a term, as A000203(k) = 349491681 < 371506905 = 135*2751903 = A000005(k)*A009194(k).

k = 866849445 = 5 * 3^4 * 7^2 * 11^2 * 19^2 is a term, as A000203(k) = 2096950086 < 2229041430 = 270*8255709 = A000005(k)*A009194(k).

PROG

(PARI) is_A388269(k) = if(!(k%2), 0, my(f=factor(k)); numdiv(f) >= numerator(sigma(f, -1)));