A329619 - OEIS

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A329619

Difference between the maximal digit value used when A108951(n) is written in primorial base and its 2-adic valuation.

1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, 0, 4, -2, 0, -1, 0, 1, 4, 0, 0, -1, 2, 0, -2, 1, 0, 2, 0, -4, 4, 0, 6, 0, 0, 0, 4, -3, 0, -2, 0, 1, 2, 0, 0, -2, 4, 5, 4, 1, 0, -2, 2, 4, 4, 0, 0, -1, 0, 0, 0, -4, 11, 9, 0, 1, 4, 2, 0, -2, 0, 0, 2, 1, 14, 9, 0, -3, 2, 0, 0, -2, 9, 0, 4, 4, 0, 6, 10, 1, 4, 0, 5, 0, 0, 9, 7, 2, 0, 9, 0, 4, 1

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OFFSET

1,8

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 primorial base

Index entries for sequences related to primorial numbers

FORMULA

a(n) = A329344(n) - A001222(n).

a(n) = A328114(A108951(n)) - A007814(A108951(n)).

a(p) = 0 for all primes p.

MATHEMATICA

With[{b = Reverse@ Prime@ Range@ 120}, Array[Max@ IntegerDigits[#, MixedRadix[b]] &@ Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] - PrimeOmega[#] &, 105] ] (* Michael De Vlieger, Nov 18 2019 *)

PROG

(PARI)

A034386(n) = prod(i=1, primepi(n), prime(i));

A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951

A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };

A329344(n) = A328114(A108951(n));

A329619(n) = (A329344(n) - bigomega(n));

CROSSREFS

Cf. A001222, A007814, A034386, A108951, A276086, A324886, A328114, A329344, A329618, A329620, A329622.

Sequence in context: A140728 A254110 A331289 * A298426 A130068 A316825

Adjacent sequences: A329616 A329617 A329618 * A329620 A329621 A329622

KEYWORD

sign

AUTHOR

Antti Karttunen, Nov 18 2019

STATUS

approved