

A339667


Number of nonempty subsets of divisors of n having a common factor > 1.


0



0, 1, 1, 3, 1, 5, 1, 7, 3, 5, 1, 19, 1, 5, 5, 15, 1, 19, 1, 19, 5, 5, 1, 71, 3, 5, 7, 19, 1, 37, 1, 31, 5, 5, 5, 111, 1, 5, 5, 71, 1, 37, 1, 19, 19, 5, 1, 271, 3, 19, 5, 19, 1, 71, 5, 71, 5, 5, 1, 347, 1, 5, 19, 63, 5, 37, 1, 19, 5, 37, 1, 703, 1, 5, 19, 19, 5, 37, 1, 271
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OFFSET

1,4


LINKS

Table of n, a(n) for n=1..80.
Index entries for sequences related to divisors of numbers


FORMULA

a(n) = Sum_{dn, d < n} mu(n/d) * (2^tau(d)  1), where tau = A000005.
a(n) = A100587(n)  A076078(n).
a(p) = 1 for p prime.


EXAMPLE

a(12) = 19 subsets: {2}, {3}, {4}, {6}, {12}, {2, 4}, {2, 6}, {2, 12}, {3, 6}, {3, 12}, {4, 6}, {4, 12}, {6, 12}, {2, 4, 6}, {2, 4, 12}, {2, 6, 12}, {3, 6, 12}, {4, 6, 12} and {2, 4, 6, 12}.


MATHEMATICA

Table[DivisorSum[n, MoebiusMu[n/#] (2^DivisorSigma[0, #]  1) &, # < n &], {n, 80}]


CROSSREFS

Cf. A000005, A027750, A076078, A100587, A109511.
Sequence in context: A093411 A147088 A340083 * A322993 A118402 A122383
Adjacent sequences: A339664 A339665 A339666 * A339668 A339669 A339670


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 12 2020


STATUS

approved



