A349755 Numbers k for which the 3-adic valuations of k and sigma(k) are equal, and that also satisfy Euler's criterion for odd perfect numbers (see A228058).

153, 325, 801, 925, 1525, 1573, 1773, 1825, 2097, 2205, 2425, 2725, 3757, 3825, 3925, 4041, 4477, 4525, 4689, 4825, 5013, 5725, 6025, 6877, 6925, 6957, 7381, 7605, 7825, 7929, 8125, 8425, 8577, 8725, 8833, 9325, 9549, 9873, 9925, 10225, 10525, 10693, 10825, 10933, 11425, 11493, 11737, 12789, 13189, 13437, 13525

Offset

1,1

Comments

Obviously, all odd perfect numbers x, if such numbers exist at all, have to satisfy not only the famous condition given by Euler (see A228058), but also valuation(sigma(x), p) = valuation(x, p) for all odd primes p = 3, 5, 7, 11, etc. See also comments in A349752.

a(109), a(283), a(440) = 31213, 88837, 146461, are the first terms not occurring in A387162. - Antti Karttunen, Aug 27 2025

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

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

Index entries for sequences related to sigma(n)

Prog

(PARI)
isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
isA349755(n) = (isA228058(n)&&valuation(sigma(n), 3)==valuation(n, 3));

Crossrefs

Intersection of A228058 and A349749.

Cf. A387162 (subsequence).

Cf. A000203, A007949, A349752.

Sequence in context: A348938 A159294 A332228 * A387162 A066528 A046197

Adjacent sequences: A349752 A349753 A349754 * A349756 A349757 A349758

Keyword

nonn

Author

Antti Karttunen, Dec 02 2021

Status

approved