The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A371733

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A371733

Maximal length of a factorization of n into factors > 1 all having the same sum of prime indices.
(history; published version)

#18 by OEIS Server at Mon Jan 20 22:52:46 EST 2025

LINKS

Antti Karttunen, <a href="/A371733/b371733_1.txt">Table of n, a(n) for n = 1..65537</a>

#17 by N. J. A. Sloane at Mon Jan 20 22:52:46 EST 2025

STATUS

proposed

approved

Discussion

Mon Jan 20

22:52

OEIS Server: Installed first b-file as b371733.txt.

#16 by Antti Karttunen at Mon Jan 20 16:37:22 EST 2025

STATUS

editing

proposed

Discussion

Mon Jan 20

17:19

Antti Karttunen: I think I will call it a day now... Thanks!

17:19

Antti Karttunen: (after these last five).

#15 by Antti Karttunen at Mon Jan 20 16:37:15 EST 2025

LINKS

Antti Karttunen, <a href="/A371733/b371733_1.txt">Table of n, a(n) for n = 1..65537</a>

<a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

#14 by Antti Karttunen at Mon Jan 20 16:34:53 EST 2025

DATA

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 5, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4

PROG

(PARI)

A056239(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1])));

all_have_same_sum_of_pis(facs) = if(!#facs, 1, (#Set(apply(A056239, facs)) == 1));

A371733(n, m=n, facs=List([])) = if(1==n, if(all_have_same_sum_of_pis(facs), #facs, 0), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s = max(s, A371733(n/d, d, newfacs)))); (s)); \\ Antti Karttunen, Jan 20 2025

EXTENSIONS

Data section extended to a(108) by Antti Karttunen, Jan 20 2025

STATUS

approved

editing

#13 by Peter Luschny at Sun Apr 14 03:49:49 EDT 2024

STATUS

reviewed

approved

#12 by Joerg Arndt at Sun Apr 14 03:02:57 EDT 2024

STATUS

proposed

reviewed

#11 by Gus Wiseman at Sun Apr 14 01:35:35 EDT 2024

STATUS

editing

proposed

#10 by Gus Wiseman at Sun Apr 14 01:35:17 EDT 2024

COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Sum of prime indices is given by A056239.

STATUS

proposed

editing

#9 by Gus Wiseman at Sun Apr 14 01:31:02 EDT 2024

STATUS

editing

proposed