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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 Antti Karttunen, Table of n, a(n) for n = 1..65537 Index entries for sequences computed from indices in prime factorization Index entries for sequences related to sigma(n) 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 Adjacent sequences: A336929 A336930 A336931 * A336933 A336934 A336935 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.)