A353268 The least number with the same prime factorization pattern (A348717) as A329603(n) = A005940(1+(1+(3*A156552(n)))).

2, 2, 8, 6, 18, 2, 50, 12, 20, 8, 98, 14, 242, 18, 32, 24, 338, 6, 578, 54, 72, 50, 722, 28, 42, 98, 60, 150, 1058, 2, 1682, 48, 200, 242, 162, 70, 1922, 338, 392, 108, 2738, 8, 3362, 294, 44, 578, 3698, 56, 110, 20, 968, 726, 4418, 12, 450, 300, 1352, 722, 5618, 26, 6962, 1058, 500, 96, 882, 18, 7442, 1014, 2312

Offset

1,1

Links

Table of n, a(n) for n=1..69.

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A348717(A329603(n)).

For all n >= 1, a(2n) = A352892(2n), a(2n-1) = A329603(2n-1).

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A329603(n) = A005940(2+(3*A156552(n)));
A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
A353268(n) = A348717(A329603(n));

Crossrefs

Cf. A005940, A156552, A348717, A353267.

Coincides with A352892 on even n, and with A329603 on odd n.

Sequence in context: A067436 A285114 A071418 * A245582 A361790 A197820

Adjacent sequences: A353265 A353266 A353267 * A353269 A353270 A353271

Keyword

nonn

Author

Antti Karttunen, Apr 09 2022

Status

approved