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A195150 Number of divisors d of n such that d-1 does not divide n. 3
0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 3, 3, 1, 3, 1, 3, 3, 2, 1, 4, 2, 2, 3, 4, 1, 4, 1, 4, 3, 2, 3, 5, 1, 2, 3, 5, 1, 4, 1, 4, 5, 2, 1, 6, 2, 4, 3, 4, 1, 5, 3, 5, 3, 2, 1, 6, 1, 2, 5, 5, 3, 5, 1, 4, 3, 6, 1, 7, 1, 2, 5, 4, 3, 5, 1, 7, 4, 2, 1, 7, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Define "subdivisor" of n to be the positive integer b such that b = d - 1, if d divides n and b does not divide n. For the list of subdivisors of n see A195153.

First occurrence of k=0.. for n: 1, 3, 8, 15, 24, 36, 48, 72, 96, ..., = A173569(k+1). - Robert G. Wilson v, Sep 23 2011

LINKS

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

FORMULA

a(n)=A137921(n)-1. - Robert G. Wilson v, Sep 23 2001

EXAMPLE

a(24) = 4 since the divisors of 24 are 1,2,3,4,6,8,12,24, so the subdivisors of 24 are 5,7,11,23 because 6-1 = 5, 8-1 = 7, 12-1 = 11 and 24-1 = 23. Note that the positive integers 1,2,3 are not subdivisors of 24 because they are divisors of 24.

MATHEMATICA

f[n_] := Module[{d = Divisors[n]}, Length[Select[Rest[d-1], Mod[n, #] > 0 &]]]; Table[f[n], {n, 100}] (* T. D. Noe, Sep 22 2011 *)

PROG

(Haskell)

a195150 n = length [d | d <- [3..n], mod n d == 0, mod n (d-1) /= 0]

-- Reinhard Zumkeller, Sep 23 2011

CROSSREFS

Cf. A000005, A027750, A066272, A195153, A137921, A173569.

Sequence in context: A280314 A080354 A238529 * A022307 A029413 A237523

Adjacent sequences:  A195147 A195148 A195149 * A195151 A195152 A195153

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 19 2011

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)