A372567 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).

135, 285, 435, 455, 675, 855, 885, 945, 1185, 1287, 1305, 1335, 1365, 1425, 1435, 1485, 1635, 1755, 1995, 2085, 2175, 2235, 2275, 2295, 2565, 2655, 2685, 2905, 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

Offset: 1

Author

Antti Karttunen, May 19 2024

Keywords

• nonn

Comments

Most seem to be multiples of 5.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Odd terms in A372566.

Cf. A000203, A003961, A349176 (subsequence).

Cf. also conjecture 1 in A349753.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA372567(n) = ((n%2) && (1A003961(n)])));