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Numbers k such that the odd parts of sigma(k) and A064989(k) are equal, where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.
2

%I #12 Jul 12 2024 14:23:41

%S 1,3,5,15,189,945,2125,6375,9261,42550,46305,127650,401625,936100,

%T 1191400,2808300,3574200,8041950,19679625,22469750,58378600,58506250,

%U 67409250,175135800,175518750,176922900,394055550,494334500

%N Numbers k such that the odd parts of sigma(k) and A064989(k) are equal, where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

%C Odd terms after 1 form a subsequence of A347391.

%C If x and y are included, and they are coprime (gcd(x,y) = 1), then x*y is also included.

%F {k | A000265(sigma(k)) = A000265(A064989(k))}.

%e 945 = 3^3 * 5 * 7 is included as A064989(945) = 2^3 * 3 * 5 = 120, and sigma(945) = 1920 = 2^7 * 3 * 5, with A000265(120) = A000265(1920) = 15.

%o (PARI) isA374463(n) = (A000265(sigma(n)==A000265(A064989(n))));

%Y Cf. A000203, A000265, A064989, A161942, A347391, A374464.

%K nonn,more

%O 1,2

%A _Antti Karttunen_, Jul 11 2024