A344978 Numbers k such that A011772(k) is equal to A344878(k), but k is not a power of prime.

21, 26, 39, 50, 57, 74, 75, 78, 93, 98, 111, 122, 129, 146, 147, 150, 183, 194, 201, 205, 218, 219, 222, 237, 242, 291, 294, 301, 305, 309, 314, 327, 338, 362, 363, 366, 381, 386, 405, 417, 438, 452, 453, 458, 471, 482, 489, 505, 507, 543, 554, 578, 579, 582, 597, 605, 610, 626, 633, 654, 657, 669, 674, 676, 687

Offset: 1

Author

Antti Karttunen, Jun 04 2021

Keywords

• nonn

Comments

Numbers k for which A344976(k) = 0, and A001221(k) > 1.

Crossrefs

Cf. A000961, A001221, A011772, A344878, A344970, A344976.

Subsequence of A344975. Intersection of A024619 and A344979.

Programs

PARI

A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
A344878(n) = if(1==n,n, my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^(f[2, i]+(2==f[1, i]))-1))));
isA344978(n) = (omega(n)>1&&(A344878(n)==A011772(n)));

Formula

For all n, A344970(a(n)) = 1.