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A344592
a(n) = A003557(A276086(A108951(n))).
10
1, 1, 1, 3, 1, 5, 1, 1, 1, 7, 1, 125, 1, 11, 16807, 15, 1, 35, 1, 343, 161051, 13, 1, 25, 9317, 17, 1, 1331, 1, 2401, 1, 1, 371293, 19, 253333223, 42875, 1, 23, 1419857, 1, 1, 1, 1, 2197, 14641, 29, 1, 49, 371293, 6684099653, 2476099, 4913, 1, 55, 37349, 19487171, 6436343, 31, 1, 5929, 1, 37, 20449, 21, 582622237229761, 1792160394037
OFFSET
1,4
FORMULA
a(n) = A329047(n) / A342920(n).
a(n) = A085731(A324886(n)) = gcd(A324886(n), A329047(n)) = A324886(n) / A346091(n). - Antti Karttunen, Jul 09 2021
MATHEMATICA
Block[{b = MixedRadix[Reverse@ Prime@ Range@ 20]}, Array[#/(Times @@ FactorInteger[#][[All, 1]]) &@ Apply[Times, Power @@@ #] &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[#, b] &@ Apply[Times, Map[(Times @@ Prime@ Range@ PrimePi@ #1)^#2 & @@ # &, FactorInteger[#]]] &, 66]] (* Michael De Vlieger, Jul 14 2021 *)
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
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
(PARI)
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
CROSSREFS
Cf. A344591 (positions of ones), A344593 (rgs-transform).
Sequence in context: A143069 A010286 A340074 * A176801 A339903 A187367
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 26 2021
STATUS
approved