The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A078174 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A078174

Numbers with an integer arithmetic mean of distinct prime factors.
(history; published version)

#18 by Charles R Greathouse IV at Mon Nov 07 20:11:25 EST 2022

STATUS

editing

approved

#17 by Charles R Greathouse IV at Mon Nov 07 20:11:23 EST 2022

PROG

(PARI) is(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i])%#f==1 0 \\ Charles R Greathouse IV, May 30 2013

STATUS

approved

editing

#16 by Susanna Cuyler at Sat Nov 16 20:04:09 EST 2019

STATUS

proposed

approved

#15 by Gus Wiseman at Sat Nov 16 18:47:55 EST 2019

STATUS

editing

proposed

#14 by Gus Wiseman at Sat Nov 16 14:49:59 EST 2019

CROSSREFS

Cf. A001221, A001414, A067629, A112798, A316413, A316428, A326567/A326568, A326622A328966.

#13 by Gus Wiseman at Sat Nov 16 14:13:09 EST 2019

CROSSREFS

Positions of 1's in A123529A323172.

#12 by Gus Wiseman at Sat Nov 16 13:49:26 EST 2019

CROSSREFS

Cf. A078175.

#11 by Gus Wiseman at Sat Nov 16 13:49:07 EST 2019

CROSSREFS

Positions of 1's in A123529.

The version counting multiplicity is A078175.

The version for prime indices is A326621.

The average of the set of distinct prime factors is A323171/A323172.

The average of the multiset of prime factors is A123528/A123529.

Cf. A001221, A001414, A067629, A112798, A316413, A316428, A326567/A326568, A326622.

STATUS

approved

editing

#10 by Harvey P. Dale at Mon Apr 18 09:44:11 EDT 2016

STATUS

editing

approved

#9 by Harvey P. Dale at Mon Apr 18 09:44:07 EDT 2016

MATHEMATICA

Select[Range[2, 200], IntegerQ[Mean[Transpose[FactorInteger[#]][[1]]]]&] (* Harvey P. Dale, Apr 18 2016 *)

STATUS

approved

editing