A158975 a(n) = sum of numbers k <= n such that all proper divisors of k are divisors of n.

1, 3, 6, 10, 11, 21, 18, 30, 27, 32, 29, 68, 42, 60, 66, 70, 59, 96, 78, 120, 108, 104, 101, 180, 126, 131, 137, 155, 130, 229, 161, 221, 203, 199, 221, 281, 198, 240, 246, 321, 239, 335, 282, 360, 403, 332, 329, 488, 378, 418, 389, 419, 382, 500, 462, 557, 448

Offset: 1

Author

Jaroslav Krizek, Apr 01 2009

Keywords

• nonn

Comments

For primes p, a(p) = A158662(p) = A014284(A036234(p)).

Examples

			For n = 8 we have the following proper divisors of k <= n: {1}, {1}, {1}, {1, 2}, {1}, {1, 2, 3}, {1}, {1, 2, 4}. Only k = 6 has a proper divisor that is not a divisor of 8, viz. 3. Hence a(8) = 1 + 2 + 3 + 4 + 5 + 7 + 8 = 30.
		

Crossrefs

Cf. A000040, A158662, A014284, A036234, 158973.

Programs

Magma

[ &+[ k: k in [1..n] | forall(t){ d: d in Divisors(k) | d eq k or d in Divisors(n) } ]: n in [1..57] ];

Extensions

Edited and extended by Klaus Brockhaus, Apr 06 2009