The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A110878 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A110878

Positive integers k such that the sum of the divisors of k, excluding 1, is a multiple of the number of divisors of k.
(history; published version)

#21 by Joerg Arndt at Sat Feb 24 01:12:24 EST 2024

STATUS

editing

approved

#20 by Paolo P. Lava at Fri Feb 23 16:01:11 EST 2024

FORMULA

k such that A000203(k) mod A000005(k) = 1. [Paolo P. Lava, Jan 31 2013]

MAPLE

with(numtheory);

A110878:=proc(q)

local n;

for n from 1 to q do if (sigma(n) mod tau(n))=1 then print(n);

fi; od; end:

A110878(100000000); # Paolo P. Lava, Jan 31 2013

STATUS

approved

editing

#19 by Harvey P. Dale at Wed Dec 23 13:37:22 EST 2020

STATUS

editing

approved

#18 by Harvey P. Dale at Wed Dec 23 13:37:19 EST 2020

MATHEMATICA

Select[Range[20000], Divisible[DivisorSigma[1, #]-1, DivisorSigma[0, #]]&] (* Harvey P. Dale, Dec 23 2020 *)

STATUS

approved

editing

#17 by Susanna Cuyler at Sat Jan 19 22:17:35 EST 2019

STATUS

proposed

approved

#16 by Jon E. Schoenfield at Sat Jan 19 20:16:00 EST 2019

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Sat Jan 19 20:15:57 EST 2019

NAME

Positive integers n k such that the sum of the divisors of n, k, excluding 1, is a multiple of the number of divisors of nk.

FORMULA

n k such that A000203(nk) mod A000005(nk) = 1. [Paolo P. Lava, Jan 31 2013]

EXAMPLE

The 9 divisors of 36 are {1,2,3,4,6,9,12,18,36}, giving sigma(36)-1=90 , which is a multiple of 9. Thus 36 is a term of the sequence.

MAPLE

A110878(100000000); # Paolo P. Lava, Jan 31 2013.

STATUS

approved

editing

#14 by T. D. Noe at Fri Feb 01 12:10:53 EST 2013

STATUS

proposed

approved

#13 by Joerg Arndt at Fri Feb 01 10:09:05 EST 2013

STATUS

editing

proposed

#12 by Joerg Arndt at Fri Feb 01 10:08:58 EST 2013

FORMULA

n such that A000203(n) mod A000005(n) = 1. [Paolo P. Lava, Jan 31 2013]

STATUS

proposed

editing