

A158975


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


1



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
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..57.


EXAMPLE

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.


PROG

(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] ];


CROSSREFS

Cf. A000040, A158662, A014284, A036234, 158973.
Sequence in context: A105359 A105355 A183545 * A282876 A261662 A050107
Adjacent sequences: A158972 A158973 A158974 * A158976 A158977 A158978


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Apr 01 2009


EXTENSIONS

Edited and extended by Klaus Brockhaus, Apr 06 2009


STATUS

approved



