The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A335452

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A335452

Number of separations (Carlitz compositions or anti-runs) of the prime indices of n.
(history; published version)

#12 by Alois P. Heinz at Wed Feb 03 13:47:03 EST 2021

STATUS

proposed

approved

#11 by Andrew Howroyd at Wed Feb 03 13:24:50 EST 2021

STATUS

editing

proposed

#10 by Andrew Howroyd at Wed Feb 03 13:19:12 EST 2021

COMMENTS

a(n) depends only on the prime signature of n. - Andrew Howroyd, Feb 03 2021

LINKS

Andrew Howroyd, <a href="/A335452/b335452.txt">Table of n, a(n) for n = 1..4096</a>

PROG

(PARI)

F(i, j, r, t) = {sum(k=max(0, i-j), min(min(i, t), (i-j+t)\2), binomial(i, k)*binomial(r-i+1, t+i-j-2*k)*binomial(t-1, k-i+j))}

count(sig)={my(s=vecsum(sig), r=0, v=[1]); for(p=1, #sig, my(t=sig[p]); v=vector(s-r-t+1, j, sum(i=1, #v, v[i]*F(i-1, j-1, r, t))); r += t); v[1]}

a(n)={count(factor(n)[, 2])} \\ Andrew Howroyd, Feb 03 2021

STATUS

approved

editing

#9 by Susanna Cuyler at Mon Jun 22 01:53:48 EDT 2020

STATUS

proposed

approved

#8 by Gus Wiseman at Sun Jun 21 23:26:01 EDT 2020

STATUS

editing

proposed

#7 by Gus Wiseman at Sun Jun 21 01:33:40 EDT 2020

CROSSREFS

Cf. A000961, A005117, A056239, A112798, A181796, A261962, A333221, A335451, A335454, A335465, A335489.

#6 by Gus Wiseman at Sun Jun 21 01:22:44 EDT 2020

CROSSREFS

Inseparable partitions are counted by A325535 and ranked by A335448 (positions of zeros).

#5 by Gus Wiseman at Sun Jun 21 01:21:51 EDT 2020

CROSSREFS

Positions of zeros are A335448.

Inseparable partitions are counted by A325535 and ranked by A335448 (positions of zeros).

#4 by Gus Wiseman at Sun Jun 21 01:18:03 EDT 2020

CROSSREFS

Separations are counted by A003242 and ranked by A333489.

Carlitz compositions (separations, anti-runs) are counted by A003242 and ranked by A333489 stc_anti_run.

Strict permutations are counted by A335489.

Cf. A000961, A005117, A056239, A112798, A181796, A333221, A335451, A335454, A335465, A335489.

#3 by Gus Wiseman at Sun Jun 21 01:11:49 EDT 2020

CROSSREFS

Cf. A000961, A005117, A056239, A056986, A112798, A181796, A333221, A335451, A335454, A335460, A335462, A335465.