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 A107925 Odd numbers k such that k^2 is an arithmetic number. 5
 1, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 91, 97, 103, 109, 121, 127, 133, 139, 151, 157, 163, 181, 193, 199, 211, 217, 223, 229, 241, 247, 259, 271, 277, 283, 301, 307, 313, 331, 337, 349, 367, 373, 379, 397, 403, 409, 421, 427, 433, 439, 457, 463, 469, 481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, odd numbers k such that the arithmetic and geometric means of the divisors of k^2 are both integer. Even numbers with this property are more rare and given by A107924. Contains A002476 as a subsequence. From Jianing Song, Apr 25 2022: (Start) For p prime, p^(k-1) is a term in A003601 if and only if (p^k-1)/(p-1) is divisible by k. So p^e is a term here if and only if k | (p^k-1)/(p-1) for k = 2*e+1. (Note that p cannot be equal to 2 if k | (p^k-1)/(p-1).) If a,b are both here, gcd(a,b) = 1, then a*b is also here. If a is A107924 and b is here, gcd(a,b) = 1, then a*b is also in A107924. Let r >= 1, p_1, p_2, ..., p_r be distinct primes, k_1, k_2, ..., k_r be odd numbers such that Product_{i=1..r} (p_i)^(k_i) is an arithmetic number. Then there exists a number i in 1..r such that (p_i)^(k_i) is an arithmetic number. See my link for a proof. (End) LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Jianing Song, Notes on A107925 MATHEMATICA Select[Range[1, 500, 2], Mod[DivisorSigma[1, #^2], DivisorSigma[0, #^2]]==0&] CROSSREFS Cf. A002476, A003601, A107924. Sequence in context: A038590 A218146 A129389 * A002476 A123365 A144921 Adjacent sequences: A107922 A107923 A107924 * A107926 A107927 A107928 KEYWORD easy,nonn AUTHOR Zak Seidov, Jun 10 2005 STATUS approved

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Last modified November 30 03:08 EST 2023. Contains 367452 sequences. (Running on oeis4.)