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A336932 The 2-adic valuation of A003973(n), the sum of divisors of prime shifted n. 6
0, 2, 1, 0, 3, 3, 2, 3, 0, 5, 1, 1, 1, 4, 4, 0, 2, 2, 3, 3, 3, 3, 1, 4, 0, 3, 2, 2, 5, 6, 1, 2, 2, 4, 5, 0, 1, 5, 2, 6, 2, 5, 4, 1, 3, 3, 1, 1, 0, 2, 3, 1, 2, 4, 4, 5, 4, 7, 1, 4, 2, 3, 2, 0, 4, 4, 3, 2, 2, 7, 1, 3, 4, 3, 1, 3, 3, 4, 2, 3, 0, 4, 1, 3, 5, 6, 6, 4, 1, 5, 3, 1, 2, 3, 6, 3, 1, 2, 1, 0, 3, 5, 2, 4, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Additive with a(p^2e) = 0, a(p^(2e-1)) = A007814(1+A003961(p)) + A007814(e).
a(n) = A007814(A003973(n)).
a(n) = A336937(A003961(n)).
For all n >= 1, a(n) >= A295664(n).
PROG
(PARI) A336932(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); valuation(sigma(factorback(f)), 2); };
(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)); };
(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
CROSSREFS
Cf. A000203, A000290 (positions of zeros), A003961, A003973, A007814, A295664, A336937.
Sequence in context: A347277 A357734 A228821 * A127258 A154557 A049242
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 16 2020
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)