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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).
2
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.
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.
Sequence in context: A348938 A159294 A332228 * A066528 A046197 A271730
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 02 2021
STATUS
approved