A372566 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).

6, 18, 24, 30, 42, 54, 60, 66, 72, 78, 90, 96, 102, 114, 120, 126, 132, 135, 138, 140, 150, 162, 168, 174, 180, 186, 198, 204, 210, 216, 222, 234, 240, 246, 258, 264, 270, 276, 282, 285, 288, 294, 306, 312, 318, 330, 342, 348, 354, 360, 366, 378, 384, 390, 396, 402, 408, 414, 420, 426, 435, 438, 450, 455, 456, 462

Offset: 1

Author

Antti Karttunen, May 19 2024

Keywords

• nonn

Examples

			24 = 2^3 * 3, sigma(24) = 60 = 2^2 * 3 * 5, and A003961(24) = 135 = 3^3 * 5, have 3 as their common divisor, therefore 24 is present in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961.

Positions of terms > 1 in A372565.

Subsequence of each of the following sequences: A069059, A104210, A349166, A379477.

Cf. A372567 (odd terms), A379475 (characteristic function).

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA372566(n) = (1A003961(n)]));