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A077217 Prime(k) such that the prime power with largest exponent that divides the product P(k) of composite numbers between prime(k) and prime(k+1) is an odd number, i.e., if p^r and 2^s divide P(k) then r >= s, p is an odd prime. 1
2, 5, 17, 29, 41, 101, 107, 137, 149, 179, 197, 269, 281, 457, 461, 499, 521, 569, 593, 617, 641, 673, 727, 809, 821, 827, 857, 881, 1049, 1061, 1229, 1277, 1289, 1301, 1321, 1451, 1453, 1481, 1483, 1619, 1697, 1721, 1753, 1777, 1861, 1873, 1877, 1949, 1997, 2027 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
In most cases a power of 2 has a larger exponent than any odd prime power.
Primes p = prime(k) such that A051903(A000265(A061214(k))) >= A007814(A061214(k)). - Amiram Eldar, Apr 01 2021
LINKS
EXAMPLE
5 is a member as 6 is divisible by 3^1 as well as by 2^1.
17 is a member as 18 is divisible by 3^2 but not by 2^2.
MATHEMATICA
q[p_] := Module[{prod = Product[k, {k, p + 1, NextPrime[p] - 1}], e2}, e2 = IntegerExponent[prod, 2]; Max[FactorInteger[prod/2^e2][[;; , 2]]] >= e2]; Select[Range[2000], PrimeQ[#] && q[#] &] (* Amiram Eldar, Apr 01 2021 *)
PROG
(PARI) f(p) = prod(k=p+1, nextprime(p+1)-1, k); \\ A061214
isok(p) = {my(prd = f(p), e = valuation(prd, 2), ofprd = prd/2^e); if (prd > 1, (ofprd == 1) || (e <= vecmax(factor(ofprd)[, 2]))); } \\ Michel Marcus, Apr 01 2021
CROSSREFS
Sequence in context: A277208 A243183 A195271 * A120847 A244085 A019353
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 02 2002
EXTENSIONS
Wrong term removed and more terms added by Amiram Eldar, Apr 01 2021
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)