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Revision History for A336932

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

A336932

The 2-adic valuation of A003973(n), the sum of divisors of prime shifted n.
(history; published version)

#12 by N. J. A. Sloane at Tue Jul 05 23:30:48 EDT 2022

STATUS

proposed

approved

#11 by Chai Wah Wu at Tue Jul 05 20:23:04 EDT 2022

STATUS

editing

proposed

#10 by Chai Wah Wu at Tue Jul 05 20:23:00 EDT 2022

PROG

(Python)

from math import prod

from sympy import factorint, nextprime

def A336932(n): return (~(m:=prod(((q:=nextprime(p))**(e+1)-1)//(q-1) for p, e in factorint(n).items()))& m-1).bit_length() # Chai Wah Wu, Jul 05 2022

STATUS

approved

editing

#9 by Susanna Cuyler at Sun Aug 16 19:59:39 EDT 2020

STATUS

proposed

approved

#8 by Antti Karttunen at Sun Aug 16 14:09:44 EDT 2020

STATUS

editing

proposed

#7 by Antti Karttunen at Sun Aug 16 14:06:09 EDT 2020

FORMULA

For all n >= 1, a(n) >= A295664(n).

CROSSREFS

Cf. A000203, A000290 (positions of zeros), A003961, A003973, A007814, A295664, A336937.

#6 by Antti Karttunen at Sun Aug 16 13:50:54 EDT 2020

LINKS

<a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

<a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

#5 by Antti Karttunen at Sun Aug 16 13:49:22 EDT 2020

LINKS

Antti Karttunen, <a href="/A336932/b336932.txt">Table of n, a(n) for n = 1..65537</a>

CROSSREFS

Cf. A000203, A000290 (positions of zeros), A003961, A003973, A007814, A336937.

#4 by Antti Karttunen at Sun Aug 16 13:44:43 EDT 2020

PROG

(PARI)

A007814(n) = valuation(n, 2);

A336932(n) = { my(f=factor(n)); sum(i=1, #f~, (f[i, 2]%2) * (A007814(1+nextprime(1+f[i, 1]))+A007814(1+f[i, 2])-1)); };

#3 by Antti Karttunen at Sun Aug 16 13:41:33 EDT 2020

FORMULA

Additive with a(p^2e) = 0, a(p^(2e-1)) = A007814(1+A003961(p)) + A007814(e).