A372567 - OEIS

%I #12 May 19 2024 14:35:28

%S 135,285,435,455,675,855,885,945,1185,1287,1305,1335,1365,1425,1435,

%T 1485,1635,1755,1995,2085,2175,2235,2275,2295,2565,2655,2685,2905,

%U 2985,3045,3105,3135,3185,3311,3375,3395,3435,3555,3585,3705,3915,4005,4035,4095,4185,4235,4275,4305,4425,4725,4785,4845,4865,4905

%N Odd numbers k such that k, sigma(k) and A003961(k) have a common divisor larger than 1, where A003961(n) is fully multiplicative function with a(prime(i)) = prime(i+1).

%C Most seem to be multiples of 5.

%H Antti Karttunen, <a href="/A372567/b372567.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e 135 = 3^3 * 5, sigma(135) = 240 = 2^4 * 3 * 5, and A003961(135) = 875 = 5^3 * 7 have 5 as their common divisor, therefore 135 is present in this sequence.

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o isA372567(n) = ((n%2) && (1<gcd([n, sigma(n), A003961(n)])));

%Y Odd terms in A372566.

%Y Cf. A000203, A003961, A349176 (subsequence).

%Y Cf. also conjecture 1 in A349753.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 19 2024