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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A351555 a(n) is the number of odd prime factors of sigma(n) that do not divide A003961(n) and the valuation(n, p) is different from valuation(sigma(n), p). 6 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0 (list; graph; refs; listen; history; text; internal format) OFFSET 1,29 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) PROG (PARI) A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A351555(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); sum(k=1, #f~, if((f[k, 1]%2) && 0!=(u%f[k, 1]), (valuation(n, f[k, 1])!=f[k, 2]), 0)); }; CROSSREFS Cf. A000203, A003961, A351551, A351554 (positions of zeros), A351553 (even terms there), A351543. Sequence in context: A330005 A165277 A245194 * A215020 A103612 A083913 Adjacent sequences: A351552 A351553 A351554 * A351556 A351557 A351558 KEYWORD nonn AUTHOR Antti Karttunen, Feb 16 2022 STATUS approved

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Last modified August 18 15:25 EDT 2024. Contains 375269 sequences. (Running on oeis4.)