

A141197


a(n) = the number of divisors of n that are each one less than a power of a prime.


5



1, 2, 2, 3, 1, 4, 2, 4, 2, 3, 1, 6, 1, 3, 3, 5, 1, 5, 1, 4, 3, 3, 1, 8, 1, 3, 2, 5, 1, 7, 2, 5, 2, 2, 2, 8, 1, 2, 2, 6, 1, 6, 1, 4, 3, 3, 1, 10, 2, 3, 2, 5, 1, 5, 1, 6, 2, 3, 1, 10, 1, 3, 4, 5, 1, 6, 1, 3, 2, 5, 1, 11, 1, 2, 3, 3, 2, 6, 1, 8, 2, 3, 1, 9, 1, 2, 2, 6, 1, 8, 2, 4, 3, 2, 1, 11, 1, 3, 2, 5, 1, 5, 1
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OFFSET

1,2


COMMENTS

A067513(n) <= a(n) <= A000005(n). [From Reinhard Zumkeller, Oct 06 2008]
a(A185208(n)) = 1.  Reinhard Zumkeller, Nov 01 2012


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = sum (A010055(A027750(n,k)): k=1..A000005(n)).  Reinhard Zumkeller, Nov 01 2012


EXAMPLE

The divisors of 9 are 1,3,9. 1 is one less than 2, a power of a prime. 3 is one less than 4, a power of a prime. And 9 is one less than 10, not a power of a prime. There are therefore 2 such divisors that are each one less than a power of a prime. So a(9)=2.


MATHEMATICA

a[n_] := Select[Divisors[n], PrimeNu[# + 1] == 1 &] // Length; Table[a[n], {n, 1, 105}] (* JeanFrançois Alcover, Aug 17 2013 *)
Table[DivisorSum[n, 1 &, PrimePowerQ[# + 1] &], {n, 103}] (* Michael De Vlieger, Aug 29 2017 *)


PROG

(Haskell)
a141197 = sum . map (a010055 . (+ 1)) . a027750_row
 Reinhard Zumkeller, Nov 01 2012


CROSSREFS

Cf. A141198.
Cf. A049073.
Sequence in context: A260439 A182471 A078378 * A035207 A324829 A294618
Adjacent sequences: A141194 A141195 A141196 * A141198 A141199 A141200


KEYWORD

nonn


AUTHOR

Leroy Quet, Jun 12 2008


EXTENSIONS

Added more terms.  Steven Bi (chenhsi(AT)stanford.edu), Dec 22 2008
Added more terms (Terms 27  50). Steven Bi (chenhsi(AT)stanford.edu), Jan 09 2009
Corrected and extended by Ray Chandler, Jun 25 2009


STATUS

approved



