

A132748


a(n) = the sum of the positive nonisolated divisors of n.


6



0, 3, 0, 3, 0, 6, 0, 3, 0, 3, 0, 10, 0, 3, 0, 3, 0, 6, 0, 12, 0, 3, 0, 10, 0, 3, 0, 3, 0, 17, 0, 3, 0, 3, 0, 10, 0, 3, 0, 12, 0, 19, 0, 3, 0, 3, 0, 10, 0, 3, 0, 3, 0, 6, 0, 18, 0, 3, 0, 21, 0, 3, 0, 3, 0, 6, 0, 3, 0, 3, 0, 27, 0, 3, 0, 3, 0, 6, 0, 12, 0, 3, 0, 23, 0, 3, 0, 3, 0, 36, 0, 3, 0, 3, 0, 10, 0, 3
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OFFSET

1,2


COMMENTS

A divisor, d, of n is nonisolated if either (d1) or (d+1) divides n.
a(2n1) = 0 for all n >= 1.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000


FORMULA

a(n) = A000203(n)  A132882(n), where A000203 is sigma(n), sum of divisors of n.


EXAMPLE

The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are next to each other and 4 and 5 are next to each other. So a(20) = 1+2+4+5 = 12.


MATHEMATICA

Table[Plus @@ (Select[Divisors[n], If[ # > 1, Mod[n, #*(#  1)] == 0]  Mod[n, #*(# + 1)] == 0 &]), {n, 1, 80}] (* Stefan Steinerberger, Nov 01 2007 *)


PROG

(PARI) A132748(n) = sumdiv(n, d, ((!(n%(1+d)))((d>1)&&(!(n%(d1)))))*d); \\ Antti Karttunen, Dec 19 2018


CROSSREFS

Cf. A129308, A132747, A133565.
Sequence in context: A323135 A100258 A045763 * A022901 A055945 A138123
Adjacent sequences: A132745 A132746 A132747 * A132749 A132750 A132751


KEYWORD

nonn


AUTHOR

Leroy Quet, Aug 27 2007


EXTENSIONS

More terms from Stefan Steinerberger, Nov 01 2007
Extended by Ray Chandler, Jun 24 2008


STATUS

approved



