login
A158976
a(n) = sum of numbers k <= n such that not all proper divisors of k are divisors of n.
2
0, 0, 0, 0, 4, 0, 10, 6, 18, 23, 37, 10, 49, 45, 54, 66, 94, 75, 112, 90, 123, 149, 175, 120, 199, 220, 241, 251, 305, 236, 335, 307, 358, 396, 409, 385, 505, 501, 534, 499, 622, 568, 664, 630, 632, 749, 799, 688, 847, 857, 937, 959, 1049, 985, 1078, 1039, 1205
OFFSET
1,5
COMMENTS
For primes p, a(p) = A000217(p) - A158662(p) = A000217(p) - A014284(A036234(p)).
EXAMPLE
For n = 7 we have the following proper divisors for k <= n: {1}, {1}, {1}, {1, 2}, {1}, {1, 2, 3}, {1}. Only 4 and 6 have proper divisors that are not divisors of 7, viz. 2 and 2, 3. Hence a(7) = 4 + 6 = 10.
PROG
(Magma) [ IsEmpty(S) select 0 else &+S where S is [ k: k in [1..n] | exists(t){ d: d in Divisors(k) | d ne k and d notin Divisors(n) } ]: n in [1..57] ];
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Apr 01 2009
EXTENSIONS
Edited and extended by Klaus Brockhaus, Apr 06 2009
STATUS
approved