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

Author

Antti Karttunen, Dec 02 2021

Keywords

• nonn
• changed

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)

Crossrefs

Intersection of A228058 and A349749.

Cf. A387162 (subsequence).

Cf. A000203, A007949, A349752.

Programs

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));