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A354088
Sum of divisors function conjugated by Pythagorean prime shift: a(n) = A348747(sigma(A348746(n))).
4
1, 1, 2, 5, 7, 2, 1, 3, 31, 7, 2, 10, 4, 1, 14, 121, 6, 31, 3, 35, 2, 2, 2, 6, 106, 4, 10, 5, 19, 14, 1, 35, 4, 6, 7, 155, 14, 3, 8, 21, 8, 2, 11, 10, 217, 2, 2, 242, 38, 106, 12, 20, 31, 10, 14, 3, 6, 19, 6, 70, 29, 1, 31, 1069, 28, 4, 13, 30, 4, 7, 4, 93, 12, 14, 212, 15, 2, 8, 3, 847, 781, 8, 14, 10, 42, 11, 38
OFFSET
1,3
COMMENTS
This is variant of A326042, and like that sequence, also this one is multiplicative.
FORMULA
Multiplicative with a(p^e) = A348747((q^(e+1)-1)/(q-1)), where q = A348744(A000720(p)).
PROG
(PARI)
A348746(n) = { my(f=factor(n)); for(k=1, #f~, if(2==f[k, 1], f[k, 1]=3, if(3==f[k, 1], f[k, 1]=5, if(1==(f[k, 1]%4), for(i=1+primepi(f[k, 1]), oo, if(1==(prime(i)%4), f[k, 1]=prime(i); break)))))); factorback(f); };
A348747(n) = { my(f=factor(n)); for(k=1, #f~, if(f[k, 1]<=3, f[k, 1]--, if(5==f[k, 1], f[k, 1]=3, if(1==(f[k, 1]%4), forstep(i=primepi(f[k, 1])-1, 0, -1, if(1==(prime(i)%4), f[k, 1]=prime(i); break)))))); factorback(f); };
A354088(n) = A348747(sigma(A348746(n)));
CROSSREFS
Cf. also A326042, A354096 for variants.
Sequence in context: A010589 A024715 A296479 * A024709 A101245 A004576
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 17 2022
STATUS
approved